We investigate reinforcement learning and genetic algorithms in the context of heterotic Calabi-Y... more We investigate reinforcement learning and genetic algorithms in the context of heterotic Calabi-Yau models with monad bundles. Both methods are found to be highly efficient in identifying phenomenologically attractive three-family models, in cases where systematic scans are not feasible. For monads on the bi-cubic Calabi-Yau either method facilitates a complete search of the environment and leads to similar sets of previously unknown three-family models.
We demonstrate how quantum field theory problems can be embedded on quantum annealers. The genera... more We demonstrate how quantum field theory problems can be embedded on quantum annealers. The general method we use is a discretisation of the field theory problem into a general Ising model, with the continuous field values being encoded into Ising spin chains. To illustrate the method, and as a simple proof of principle, we use a (hybrid) quantum annealer to recover the correct profile of the thin-wall tunnelling solution. This method is applicable to many nonperturbative problems.
Proceedings of Cargèse Summer School: Cosmology and Particle Physics Beyond the Standard Models — PoS(cargese), 2009
A pedagogical introduction to string theory and string phenomenology is given. The classical and ... more A pedagogical introduction to string theory and string phenomenology is given. The classical and quantum strings are introduced using a pedagogical and pragmatic approach for a reader familiar with supersymmetric field theory. The emphasis is on deriving and understanding the phenomenological properties, chiefly the spectrum and interactions of the 5 perturbative supersymmetric theories. An overview of some recent phenomenological applications and developments is also given.
The immensity of the string landscape and the difficulty of identifying solutions that match the ... more The immensity of the string landscape and the difficulty of identifying solutions that match the observed features of particle physics have raised serious questions about the predictive power of string theory. Modern methods of optimisation and search can, however, significantly improve the prospects of constructing the standard model in string theory. In this paper we scrutinise a corner of the heterotic string landscape consisting of compactifications on Calabi-Yau threefolds with monad bundles and show that genetic algorithms can be successfully used to generate anomaly-free supersymmetric SO(10) GUTs with three families of fermions that have the right ingredients to accommodate the standard model. We compare this method with reinforcement learning and find that the two methods have similar efficacy but somewhat complementary characteristics.
We present a prescription for using the a central charge to determine the flow of a strongly coup... more We present a prescription for using the a central charge to determine the flow of a strongly coupled supersymmetric theory from its weakly coupled dual. The approach is based on the equivalence of the scale-dependent a-parameter derived from the four-dilaton amplitude with the a-parameter determined from the Lagrange multiplier method with scale-dependent R-charges. We explicitly demonstrate this equivalence for massive free N=1 superfields and for weakly coupled SQCD.
Non-topological solitons (Q-balls) are discussed in some stringy settings. Our main result is tha... more Non-topological solitons (Q-balls) are discussed in some stringy settings. Our main result is that the dielectric D-brane system of Myers admits non-abelian Q-ball solutions on their world-volume, in which N Dp-branes relax to the standard dielectric form outside the Q-ball, but assume a more diffuse configuration at its centre. We also consider how Q-balls behave in the bulk of extra-dimensional theories, or on wrapped branes. We demonstrate that they carry Kaluza-Klein charge and possess a corresponding Kaluza-Klein tower of states just as normal particles, and we discuss surface energy effects by finding exact Q-ball solutions in models with a specific logarithmic potential.
Abstract: We examine the cosmological effects of the Hagedorn phase in models where the observabl... more Abstract: We examine the cosmological effects of the Hagedorn phase in models where the observable universe is pictured as a D-brane. It is shown that, even in the absence of a cosmological constant, winding modes cause a negative ‘pressure ’ that can drive brane inflation of various types including both power law and exponential. We also find regimes in which the cosmology is stable but oscillating (a bouncing universe) with the Hagedorn phase softening the singular behavior associated with the collapse.
We construct a simple model of an SU (5) GUT with gauge mediated supersymmetry breaking from a me... more We construct a simple model of an SU (5) GUT with gauge mediated supersymmetry breaking from a metastable vacuum of a hidden sector. All mass parameters and hierarchies of our model are generated dynamically from retrofitting. This includes the µ-parameter and the GUT scale. However, as typical for simple SU (5) GUT models, proton longevity remains a problem.
We construct a supersymmetric version of the Standard Model which contains a longlived metastable... more We construct a supersymmetric version of the Standard Model which contains a longlived metastable vacuum. In this vacuum supersymmetry is broken and the electroweak symmetry is Higgsed, and we identify it with the physical ground state of the Standard Model. In our approach the metastable supersymmetry breaking (MSB) occurs directly in the SU(2)L × U(1)Y sector of the Standard Model; it does not require a separate MSB sector and in this way it departs from the usual lore. There is a direct link between the electroweak symmetry breaking and the supersymmetry breaking in our model, both effects are induced by the same Higgs fields φi, φ̃i. In order to generate sufficiently large gluino masses we have to have strong coupling in the Higgs sector, h ≫ 1. Our model results in an extremely compact low-energy effective theory at the electroweak scale with Higgs fields being very heavy, MHiggs ≫ MW and frozen at their vacuum expectation values.
Although "anomalies" sounds like it might be a somewhat peripheral aspect of quantum field theory... more Although "anomalies" sounds like it might be a somewhat peripheral aspect of quantum field theory, it turns out that their study is central to the proper understanding of symmetries and conservation laws in QFT. Anomalies also find uses in a huge variety of applications, for example; • Checking model consistency by cancellation of gauge anomalies in e.g. the Standard Model =⇒ charge quantization for example
Genetic Algorithms (GAs) are explored as a tool for probing new physics with high dimensionality.... more Genetic Algorithms (GAs) are explored as a tool for probing new physics with high dimensionality. We study the 19-dimensional pMSSM, including experimental constraints from all sources and assessing the consistency of potential signals of new physics. We show that GAs excel at making a fast and accurate diagnosis of the cross-compatibility of a set of experimental constraints in such high dimensional models. In the case of the pMSSM, it is found that only ${\cal O}(10^4)$ model evaluations are required to obtain a best fit point in agreement with much more costly MCMC scans. This efficiency allows higher dimensional models to be falsified, and patterns in the spectrum identified, orders of magnitude more quickly. As examples of falsification, we consider the muon anomalous magnetic moment, and the Galactic Centre gamma-ray excess observed by Fermi-LAT, which could in principle be explained in terms of neutralino dark matter. We show that both observables cannot be explained within t...
In this talk, I discuss our recent work concerning the construction of non-supersymmetric heterot... more In this talk, I discuss our recent work concerning the construction of non-supersymmetric heterotic string models which have exponentially suppressed dilaton tadpoles and cosmological constants, and thus greatly enhanced stability properties. The existence of such models opens the door to non-supersymmetric string model-building, and I discuss how semi-realistic string models resembling the Standard Model or any of its unified variants may be constructed within this framework. These models maintain modular invariance and exhibit a misaligned supersymmetry which ensures UV finiteness, even without spacetime supersymmetry. I also discuss the potential implications for phenomenology.
It is well-known that in scenarios with direct gauge mediation of supersymmetry breaking the mess... more It is well-known that in scenarios with direct gauge mediation of supersymmetry breaking the messenger fields significantly affect the running of Standard Model couplings and introduce Landau poles which are difficult to avoid. Among other things, this appears to remove any possibility of a meaningful unification prediction and is often viewed as a strong argument against direct mediation. We propose two ways that Seiberg duality can circumvent this problem. In the first, which we call “deflected-unification”, the SUSY-breaking hidden sector is a magnetic theory which undergoes a Seiberg duality to an electric phase. Importantly, the electric version has fewer fundamental degrees of freedom coupled to the MSSM compared to the magnetic formulation. This changes the β-functions of the MSSM gauge couplings so as to push their Landau poles above the unification scale. We show that this scenario is realised for recently suggested models of gauge mediation based on a metastable SCQD-type ...
We design and implement a quantum annealing simulation platform to observe and study dynamical pr... more We design and implement a quantum annealing simulation platform to observe and study dynamical processes in quantum field theory (QFT). Our approach encodes the field theory as an Ising model, which is then solved by a quantum annealer. As a proof of concept, we encode a scalar field theory and measure the probability for it to tunnel from the false vacuum to the true vacuum for various tunneling times, vacuum displacements, and potential profiles. The results are in accord with those predicted theoretically, showing that a quantum annealer is a promising platform for encoding QFTs. This is the first time it has been possible to measure instanton processes across a freely chosen QFT energy barrier. We argue that this novel and flexible method to study the dynamics of quantum systems has potential application to many field theories of interest. Measurements of the dynamical behavior of such encoded field theories are independent of theoretical calculations and can be used to infer their properties without being limited by the availability of suitable perturbative or nonperturbative computational methods. Soon, measurements using such a quantum annealing simulation platform could therefore be used to improve theoretical and computational methods conceptually and may enable the measurement and detailed study of previously unobserved quantum phenomena.
Achieving full moduli stabilisation in type IIB string compactifications for generic Calabi-Yau t... more Achieving full moduli stabilisation in type IIB string compactifications for generic Calabi-Yau threefolds with hundreds of Kähler moduli is notoriously hard. This is due not just to the very fast increase of the computational complexity with the number of moduli, but also to the fact that the scalar potential depends in general on the supergravity variables only implicitly. In fact, the supergravity chiral coordinates are 4cycle volume moduli but the Kähler potential is an explicit function of the 2-cycle moduli and inverting between these two variables is in general impossible. In this paper we propose a general method to fix all type IIB Kähler moduli in a systematic way by working directly in terms of 2-cycle moduli: on one side we present a 'master formula' for the scalar potential which can depend on an arbitrary number of Kähler moduli, while on the other we perform a computer-based search for critical points, introducing a hybrid Genetic/Clustering/Amoeba algorithm and other computational techniques. This allows us to reproduce several known minima, but also to discover new examples of both KKLT and LVS models, together with novel classes of LVS minima without diagonal del Pezzo divisors and hybrid vacua which share some features with KKLT and other with LVS solutions.
We study particle theories that have a tower of worldline internal degrees of freedom. Such a the... more We study particle theories that have a tower of worldline internal degrees of freedom. Such a theory can arise when the worldsheet of closed strings is dimensionally reduced to a worldline, in which case the tower is infinite with regularly spaced masses. But our discussion is significantly more general than this, and there is scope to consider all kinds of internal degrees of freedom carried by the propagating particle. For example it is possible to consider towers corresponding to other geometries, or towers with no obvious geometric interpretation that still yield a modular invariant theory. Truncated towers generate non-local particle theories that share with string theory the property of having a Gross-Mende-like saddle point in their amplitudes. This provides a novel framework for constructing exotic theories which may have desirable properties such as finiteness and modular invariance.
We consider an open-string realisation of N = 2 → N = 0 spontaneous breaking of supersymmetry in ... more We consider an open-string realisation of N = 2 → N = 0 spontaneous breaking of supersymmetry in four-dimensional Minkowski spacetime. It is based on type IIB orientifold theory compactified on T 2 × T 4 /Z 2 , with Scherk-Schwarz supersymmetry breaking implemented along T 2. We show that in the regions of moduli space where the supersymmetry breaking scale is lower than the other scales, there exist configurations with minima that have massless Bose-Fermi degeneracy and hence vanishing one-loop effective potential, up to exponentially suppressed corrections. These backgrounds describe non-Abelian gauge theories, with all open-string moduli and blowing up modes of T 4 /Z 2 stabilized, while all untwisted closed-string moduli remain flat directions. Other backgrounds with strictly positive effective potentials exist, where the only instabilities arising at one loop are associated with the supersymmetry breaking scale, which runs away. All of these backgrounds are consistent non-perturbatively.
We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkows... more We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkowski background respects wordline inversion symmetry, the particle approximation to modular invariance in string theory. This symmetry automatically yields a corresponding gravitational theory that is nonlocal, with the action containing infinite order differential operators. As a consequence, despite being a higher order derivative theory, it is ghost-free and has no degrees of freedom besides the massless spin-2 graviton of Einstein’s general relativity. By working in the linearised regime we show that the point-like singularities that afflict the (local) Einstein’s theory are smeared out.
We present BPS solutions to a general class of Wess-Zumino models which ex- tend previous results... more We present BPS solutions to a general class of Wess-Zumino models which ex- tend previous results in the literature. We discuss their relation to amplitudes on threshold, and their application to scalar domain walls in Supersymmetric QCD. We also find partial expressions for Wess-Zumino models with softly broken supersymmetry.
We investigate reinforcement learning and genetic algorithms in the context of heterotic Calabi-Y... more We investigate reinforcement learning and genetic algorithms in the context of heterotic Calabi-Yau models with monad bundles. Both methods are found to be highly efficient in identifying phenomenologically attractive three-family models, in cases where systematic scans are not feasible. For monads on the bi-cubic Calabi-Yau either method facilitates a complete search of the environment and leads to similar sets of previously unknown three-family models.
We demonstrate how quantum field theory problems can be embedded on quantum annealers. The genera... more We demonstrate how quantum field theory problems can be embedded on quantum annealers. The general method we use is a discretisation of the field theory problem into a general Ising model, with the continuous field values being encoded into Ising spin chains. To illustrate the method, and as a simple proof of principle, we use a (hybrid) quantum annealer to recover the correct profile of the thin-wall tunnelling solution. This method is applicable to many nonperturbative problems.
Proceedings of Cargèse Summer School: Cosmology and Particle Physics Beyond the Standard Models — PoS(cargese), 2009
A pedagogical introduction to string theory and string phenomenology is given. The classical and ... more A pedagogical introduction to string theory and string phenomenology is given. The classical and quantum strings are introduced using a pedagogical and pragmatic approach for a reader familiar with supersymmetric field theory. The emphasis is on deriving and understanding the phenomenological properties, chiefly the spectrum and interactions of the 5 perturbative supersymmetric theories. An overview of some recent phenomenological applications and developments is also given.
The immensity of the string landscape and the difficulty of identifying solutions that match the ... more The immensity of the string landscape and the difficulty of identifying solutions that match the observed features of particle physics have raised serious questions about the predictive power of string theory. Modern methods of optimisation and search can, however, significantly improve the prospects of constructing the standard model in string theory. In this paper we scrutinise a corner of the heterotic string landscape consisting of compactifications on Calabi-Yau threefolds with monad bundles and show that genetic algorithms can be successfully used to generate anomaly-free supersymmetric SO(10) GUTs with three families of fermions that have the right ingredients to accommodate the standard model. We compare this method with reinforcement learning and find that the two methods have similar efficacy but somewhat complementary characteristics.
We present a prescription for using the a central charge to determine the flow of a strongly coup... more We present a prescription for using the a central charge to determine the flow of a strongly coupled supersymmetric theory from its weakly coupled dual. The approach is based on the equivalence of the scale-dependent a-parameter derived from the four-dilaton amplitude with the a-parameter determined from the Lagrange multiplier method with scale-dependent R-charges. We explicitly demonstrate this equivalence for massive free N=1 superfields and for weakly coupled SQCD.
Non-topological solitons (Q-balls) are discussed in some stringy settings. Our main result is tha... more Non-topological solitons (Q-balls) are discussed in some stringy settings. Our main result is that the dielectric D-brane system of Myers admits non-abelian Q-ball solutions on their world-volume, in which N Dp-branes relax to the standard dielectric form outside the Q-ball, but assume a more diffuse configuration at its centre. We also consider how Q-balls behave in the bulk of extra-dimensional theories, or on wrapped branes. We demonstrate that they carry Kaluza-Klein charge and possess a corresponding Kaluza-Klein tower of states just as normal particles, and we discuss surface energy effects by finding exact Q-ball solutions in models with a specific logarithmic potential.
Abstract: We examine the cosmological effects of the Hagedorn phase in models where the observabl... more Abstract: We examine the cosmological effects of the Hagedorn phase in models where the observable universe is pictured as a D-brane. It is shown that, even in the absence of a cosmological constant, winding modes cause a negative ‘pressure ’ that can drive brane inflation of various types including both power law and exponential. We also find regimes in which the cosmology is stable but oscillating (a bouncing universe) with the Hagedorn phase softening the singular behavior associated with the collapse.
We construct a simple model of an SU (5) GUT with gauge mediated supersymmetry breaking from a me... more We construct a simple model of an SU (5) GUT with gauge mediated supersymmetry breaking from a metastable vacuum of a hidden sector. All mass parameters and hierarchies of our model are generated dynamically from retrofitting. This includes the µ-parameter and the GUT scale. However, as typical for simple SU (5) GUT models, proton longevity remains a problem.
We construct a supersymmetric version of the Standard Model which contains a longlived metastable... more We construct a supersymmetric version of the Standard Model which contains a longlived metastable vacuum. In this vacuum supersymmetry is broken and the electroweak symmetry is Higgsed, and we identify it with the physical ground state of the Standard Model. In our approach the metastable supersymmetry breaking (MSB) occurs directly in the SU(2)L × U(1)Y sector of the Standard Model; it does not require a separate MSB sector and in this way it departs from the usual lore. There is a direct link between the electroweak symmetry breaking and the supersymmetry breaking in our model, both effects are induced by the same Higgs fields φi, φ̃i. In order to generate sufficiently large gluino masses we have to have strong coupling in the Higgs sector, h ≫ 1. Our model results in an extremely compact low-energy effective theory at the electroweak scale with Higgs fields being very heavy, MHiggs ≫ MW and frozen at their vacuum expectation values.
Although "anomalies" sounds like it might be a somewhat peripheral aspect of quantum field theory... more Although "anomalies" sounds like it might be a somewhat peripheral aspect of quantum field theory, it turns out that their study is central to the proper understanding of symmetries and conservation laws in QFT. Anomalies also find uses in a huge variety of applications, for example; • Checking model consistency by cancellation of gauge anomalies in e.g. the Standard Model =⇒ charge quantization for example
Genetic Algorithms (GAs) are explored as a tool for probing new physics with high dimensionality.... more Genetic Algorithms (GAs) are explored as a tool for probing new physics with high dimensionality. We study the 19-dimensional pMSSM, including experimental constraints from all sources and assessing the consistency of potential signals of new physics. We show that GAs excel at making a fast and accurate diagnosis of the cross-compatibility of a set of experimental constraints in such high dimensional models. In the case of the pMSSM, it is found that only ${\cal O}(10^4)$ model evaluations are required to obtain a best fit point in agreement with much more costly MCMC scans. This efficiency allows higher dimensional models to be falsified, and patterns in the spectrum identified, orders of magnitude more quickly. As examples of falsification, we consider the muon anomalous magnetic moment, and the Galactic Centre gamma-ray excess observed by Fermi-LAT, which could in principle be explained in terms of neutralino dark matter. We show that both observables cannot be explained within t...
In this talk, I discuss our recent work concerning the construction of non-supersymmetric heterot... more In this talk, I discuss our recent work concerning the construction of non-supersymmetric heterotic string models which have exponentially suppressed dilaton tadpoles and cosmological constants, and thus greatly enhanced stability properties. The existence of such models opens the door to non-supersymmetric string model-building, and I discuss how semi-realistic string models resembling the Standard Model or any of its unified variants may be constructed within this framework. These models maintain modular invariance and exhibit a misaligned supersymmetry which ensures UV finiteness, even without spacetime supersymmetry. I also discuss the potential implications for phenomenology.
It is well-known that in scenarios with direct gauge mediation of supersymmetry breaking the mess... more It is well-known that in scenarios with direct gauge mediation of supersymmetry breaking the messenger fields significantly affect the running of Standard Model couplings and introduce Landau poles which are difficult to avoid. Among other things, this appears to remove any possibility of a meaningful unification prediction and is often viewed as a strong argument against direct mediation. We propose two ways that Seiberg duality can circumvent this problem. In the first, which we call “deflected-unification”, the SUSY-breaking hidden sector is a magnetic theory which undergoes a Seiberg duality to an electric phase. Importantly, the electric version has fewer fundamental degrees of freedom coupled to the MSSM compared to the magnetic formulation. This changes the β-functions of the MSSM gauge couplings so as to push their Landau poles above the unification scale. We show that this scenario is realised for recently suggested models of gauge mediation based on a metastable SCQD-type ...
We design and implement a quantum annealing simulation platform to observe and study dynamical pr... more We design and implement a quantum annealing simulation platform to observe and study dynamical processes in quantum field theory (QFT). Our approach encodes the field theory as an Ising model, which is then solved by a quantum annealer. As a proof of concept, we encode a scalar field theory and measure the probability for it to tunnel from the false vacuum to the true vacuum for various tunneling times, vacuum displacements, and potential profiles. The results are in accord with those predicted theoretically, showing that a quantum annealer is a promising platform for encoding QFTs. This is the first time it has been possible to measure instanton processes across a freely chosen QFT energy barrier. We argue that this novel and flexible method to study the dynamics of quantum systems has potential application to many field theories of interest. Measurements of the dynamical behavior of such encoded field theories are independent of theoretical calculations and can be used to infer their properties without being limited by the availability of suitable perturbative or nonperturbative computational methods. Soon, measurements using such a quantum annealing simulation platform could therefore be used to improve theoretical and computational methods conceptually and may enable the measurement and detailed study of previously unobserved quantum phenomena.
Achieving full moduli stabilisation in type IIB string compactifications for generic Calabi-Yau t... more Achieving full moduli stabilisation in type IIB string compactifications for generic Calabi-Yau threefolds with hundreds of Kähler moduli is notoriously hard. This is due not just to the very fast increase of the computational complexity with the number of moduli, but also to the fact that the scalar potential depends in general on the supergravity variables only implicitly. In fact, the supergravity chiral coordinates are 4cycle volume moduli but the Kähler potential is an explicit function of the 2-cycle moduli and inverting between these two variables is in general impossible. In this paper we propose a general method to fix all type IIB Kähler moduli in a systematic way by working directly in terms of 2-cycle moduli: on one side we present a 'master formula' for the scalar potential which can depend on an arbitrary number of Kähler moduli, while on the other we perform a computer-based search for critical points, introducing a hybrid Genetic/Clustering/Amoeba algorithm and other computational techniques. This allows us to reproduce several known minima, but also to discover new examples of both KKLT and LVS models, together with novel classes of LVS minima without diagonal del Pezzo divisors and hybrid vacua which share some features with KKLT and other with LVS solutions.
We study particle theories that have a tower of worldline internal degrees of freedom. Such a the... more We study particle theories that have a tower of worldline internal degrees of freedom. Such a theory can arise when the worldsheet of closed strings is dimensionally reduced to a worldline, in which case the tower is infinite with regularly spaced masses. But our discussion is significantly more general than this, and there is scope to consider all kinds of internal degrees of freedom carried by the propagating particle. For example it is possible to consider towers corresponding to other geometries, or towers with no obvious geometric interpretation that still yield a modular invariant theory. Truncated towers generate non-local particle theories that share with string theory the property of having a Gross-Mende-like saddle point in their amplitudes. This provides a novel framework for constructing exotic theories which may have desirable properties such as finiteness and modular invariance.
We consider an open-string realisation of N = 2 → N = 0 spontaneous breaking of supersymmetry in ... more We consider an open-string realisation of N = 2 → N = 0 spontaneous breaking of supersymmetry in four-dimensional Minkowski spacetime. It is based on type IIB orientifold theory compactified on T 2 × T 4 /Z 2 , with Scherk-Schwarz supersymmetry breaking implemented along T 2. We show that in the regions of moduli space where the supersymmetry breaking scale is lower than the other scales, there exist configurations with minima that have massless Bose-Fermi degeneracy and hence vanishing one-loop effective potential, up to exponentially suppressed corrections. These backgrounds describe non-Abelian gauge theories, with all open-string moduli and blowing up modes of T 4 /Z 2 stabilized, while all untwisted closed-string moduli remain flat directions. Other backgrounds with strictly positive effective potentials exist, where the only instabilities arising at one loop are associated with the supersymmetry breaking scale, which runs away. All of these backgrounds are consistent non-perturbatively.
We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkows... more We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkowski background respects wordline inversion symmetry, the particle approximation to modular invariance in string theory. This symmetry automatically yields a corresponding gravitational theory that is nonlocal, with the action containing infinite order differential operators. As a consequence, despite being a higher order derivative theory, it is ghost-free and has no degrees of freedom besides the massless spin-2 graviton of Einstein’s general relativity. By working in the linearised regime we show that the point-like singularities that afflict the (local) Einstein’s theory are smeared out.
We present BPS solutions to a general class of Wess-Zumino models which ex- tend previous results... more We present BPS solutions to a general class of Wess-Zumino models which ex- tend previous results in the literature. We discuss their relation to amplitudes on threshold, and their application to scalar domain walls in Supersymmetric QCD. We also find partial expressions for Wess-Zumino models with softly broken supersymmetry.
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Papers by Steven Abel