Starting from the previously constructed effective supergravity theory below the scale of U (1) b... more Starting from the previously constructed effective supergravity theory below the scale of U (1) breaking in orbifold compactifications of the weakly coupled heterotic string, we study the effective theory below the scale of supersymmetry breaking by gaugino and matter condensation in a hidden sector. Questions we address include vacuum stability and the masses of the various moduli fields, including those associated with flat directions at the U (1) breaking scale, and of their fermionic superpartners. The issue of soft supersymmetry-breaking masses in the observable sector presents a particularly serious challenge for this class of models. Laboratory is an equal opportunity employer.
We relate bulk fields in Randall-Sundrum AdS5 phenomenological models to the world-volume fields ... more We relate bulk fields in Randall-Sundrum AdS5 phenomenological models to the world-volume fields of probe D7 branes in the Klebanov-Witten background of type IIB string theory. The string constructions are described by AdS5×T1,1 in their near-horizon geometry, with T1,1 a 5d compact internal manifold that yields N=1 supersymmetry in the dual 4d gauge theory. The effective 5d Lagrangian description derived from the explicit string construction leads to additional features that are not usually encountered in phenomenological model building.
We show that nonperturbative lattice studies of four-dimensional N=4 Super-Yang-Mills are within ... more We show that nonperturbative lattice studies of four-dimensional N=4 Super-Yang-Mills are within reach. We use Ginsparg-Wilson fermions to avoid gluino masses and an exact implementation of the (chiral) $R$-symmetry, which greatly limits the number of counterterms that must be fine-tuned. Only bosonic operators require fine tuning, so all tunings can be done ``offline'' by a Ferrenberg-Swendsen type reweighting. We show what measurables can be used to perform the tuning.
We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fer... more We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two lattice matching technique recently advocated and exploited in Ref.
We propose a gravitational dual of "single-sector" models of supersymmetry breaking which contain... more We propose a gravitational dual of "single-sector" models of supersymmetry breaking which contain no messenger sector and naturally explain the scale of supersymmetry breaking and the fermion mass hierarchy. In five dimensions these models can be given a simple interpretation. Inspired by flux-background solutions of type IIB supergravity, a metric background that deviates from AdS 5 in the IR breaks supersymmetry, while the fermion mass hierarchy results from the wavefunction overlap of bulk fermions with a UV-confined Higgs field. The first and second generation squarks and sleptons, which are localized near the IR brane, directly feel the supersymmetry breaking and obtain masses of order 10 TeV. These are interpreted as composite states of the dual 4D theory.
Continuous Advances in QCD 2008 - Proceedings of the Conference, 2008
We report preliminary results of lattice super-Yang-Mills computations using domain wall fermions... more We report preliminary results of lattice super-Yang-Mills computations using domain wall fermions, performed at an actual rate of 1000 Gflop/s, over the course of six months, using two BlueGene/L racks at Rensselaer's CCNI supercomputing center. This has allowed us to compute the gluino condensate and string tension over a wide range of lattice parameters, setting the stage for continuum, chiral extrapolations. †
The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described ... more The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described in hep-lat/0605003 uses exact lattice chirality to decouple the massless chiral fermions from a mirror sector, whose strong dynamics is conjectured to give cutoff-scale mass to the mirror fermions without breaking the chiral gauge symmetry. In this paper, we study the mirror sector dynamics of a two-dimensional chiral gauge theory in the limit of strong Yukawa and vanishing gauge couplings, in which case it reduces to an XY model coupled to Ginsparg-Wilson fermions. For the mirror fermions to acquire cutoff-scale mass it is believed to be important that the XY model remain in its "high temperature" phase, where there is no algebraic ordering-a conjecture supported by the results of our work. We use analytic and Monte-Carlo methods with dynamical fermions to study the scalar and fermion susceptibilities, and the mirror fermion spectrum. Our results provide convincing evidence that the strong dynamics does not "break" the chiral symmetry (more precisely, that the mirror fermions do not induce algebraic ordering in two-dimensions), and that the mirror fermions decouple from the infrared physics.
We report recent results and developments from our ongoing lattice studies of N = 4 supersymmetri... more We report recent results and developments from our ongoing lattice studies of N = 4 supersymmetric Yang-Mills theory. These include a proof that only a single fine-tuning needs to be performed, so long as the moduli space is not lifted by nonperturbative effects. We extend our investigations of supersymmetry restoration in the continuum limit by initiating Monte Carlo renormalization group studies. We present additional numerical evidence that the lattice theory does not suffer from a sign problem. Finally we study the static potential, which we find to be Coulombic at both weak and strong coupling. We compare the static potential Coulomb coefficients to perturbation theory, including initial results for N = 3 colors in addition to N = 2.
This White Paper has been prepared as a planning document for the Division of High Energy Physics... more This White Paper has been prepared as a planning document for the Division of High Energy Physics of the U. S. Department of Energy. Recent progress in lattice-based studies of physics beyond the standard model is summarized, and major current goals of USQCD research in this area are presented. Challenges and opportunities associated with the recently discovered 126 GeV Higgs-like particle are highlighted. Computational resources needed for reaching important goals are described. The document was finalized on February 11, 2013 with references that are not aimed to be complete, or account for an accurate historical record of the field.
String theories in principle address the origin and values of the quark and lepton masses. Perhap... more String theories in principle address the origin and values of the quark and lepton masses. Perhaps the small values of neutrino masses could be explained generically in string theory even if it is more difficult to calculate individual values, or perhaps some string constructions could be favored by generating small neutrino masses. We examine this issue in the context of the well-known threefamily standard-like Z3 heterotic orbifolds, where the theory is well enough known to construct the corresponding operators allowed by string selection rules, and analyze the D-and F-flatness conditions. Surprisingly, we find that a simple see-saw mechanism does not arise. It is not clear whether this is a property of this construction, or of orbifolds more generally, or of string theory itself. Extended see-saw mechanisms may be allowed; more analysis will be needed to settle that issue. We briefly speculate on their form if allowed and on the possibility of alternatives, such as small Dirac masses and triplet see-saws. The smallness of neutrino masses may be a powerful probe of string constructions in general. We also find further evidence that there are only 20 inequivalent models in this class, which affects the counting of string vacua.
We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the l... more We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U (1) R symmetry is exactly preserved in the limit of vanishing bare mass. We show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.
We show that nonpertubative lattice studies of four-dimensional N =4 Super-Yang-Mills are within ... more We show that nonpertubative lattice studies of four-dimensional N =4 Super-Yang-Mills are within reach. We use Ginsparg-Wilson fermions to avoid gluino masses and an exact implementation of the (chiral) R-symmetry, which greatly limits the number of counterterms that must be fine-tuned. Only bosonic operators require fine tuning, so all tunings can be done "offline" by a Ferrenberg-Swendsen type reweighting. We show what measurables can be used to perform the tuning.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2009
Lattice N = 1 super-Yang-Mills theory formulated using Ginsparg-Wilson fermions provides a rigoro... more Lattice N = 1 super-Yang-Mills theory formulated using Ginsparg-Wilson fermions provides a rigorous non-perturbative definition of the continuum theory that requires no fine-tuning as the lattice spacing is reduced to zero. Domain wall fermions are one explicit scheme for achieving this and using them we have performed large scale Monte Carlo simulations of the theory for gauge group SU (2). We have measured the gaugino condensate, static potential, Creutz ratios and residual mass for several values of the domain wall separation L s , four-dimensional lattice volume, and two values of the bare gauge coupling. With this data we are able to extrapolate the gaugino condensate to the chiral limit, to express it in physical units, and to establish important benchmarks for future studies of super-Yang-Mills on the lattice.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2012
We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fer... more We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, γ = −0.03(13), however taking this source of systematic error into account gives a much larger range of allowed values, −0.6 γ 0.6. We also attempt to measure the anomalous mass dimension using the stability matrix method. We discuss the systematic errors affecting the current analysis and possible improvements.
We present a Monte Carlo Renormalisation Group (MCRG) study of the SU(2) gauge theory with two Di... more We present a Monte Carlo Renormalisation Group (MCRG) study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, gamma=-0.03(13), however without this assumption our uncertainty in the running of the coupling leads to a much larger range of allowed values, -0.6 < gamma < 0.6. We discuss the systematic errors affecting the current analysis and possible improvements.
Starting from the previously constructed effective supergravity theory below the scale of U (1) b... more Starting from the previously constructed effective supergravity theory below the scale of U (1) breaking in orbifold compactifications of the weakly coupled heterotic string, we study the effective theory below the scale of supersymmetry breaking by gaugino and matter condensation in a hidden sector. Questions we address include vacuum stability and the masses of the various moduli fields, including those associated with flat directions at the U (1) breaking scale, and of their fermionic superpartners. The issue of soft supersymmetry-breaking masses in the observable sector presents a particularly serious challenge for this class of models. Laboratory is an equal opportunity employer.
We relate bulk fields in Randall-Sundrum AdS5 phenomenological models to the world-volume fields ... more We relate bulk fields in Randall-Sundrum AdS5 phenomenological models to the world-volume fields of probe D7 branes in the Klebanov-Witten background of type IIB string theory. The string constructions are described by AdS5×T1,1 in their near-horizon geometry, with T1,1 a 5d compact internal manifold that yields N=1 supersymmetry in the dual 4d gauge theory. The effective 5d Lagrangian description derived from the explicit string construction leads to additional features that are not usually encountered in phenomenological model building.
We show that nonperturbative lattice studies of four-dimensional N=4 Super-Yang-Mills are within ... more We show that nonperturbative lattice studies of four-dimensional N=4 Super-Yang-Mills are within reach. We use Ginsparg-Wilson fermions to avoid gluino masses and an exact implementation of the (chiral) $R$-symmetry, which greatly limits the number of counterterms that must be fine-tuned. Only bosonic operators require fine tuning, so all tunings can be done ``offline'' by a Ferrenberg-Swendsen type reweighting. We show what measurables can be used to perform the tuning.
We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fer... more We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two lattice matching technique recently advocated and exploited in Ref.
We propose a gravitational dual of "single-sector" models of supersymmetry breaking which contain... more We propose a gravitational dual of "single-sector" models of supersymmetry breaking which contain no messenger sector and naturally explain the scale of supersymmetry breaking and the fermion mass hierarchy. In five dimensions these models can be given a simple interpretation. Inspired by flux-background solutions of type IIB supergravity, a metric background that deviates from AdS 5 in the IR breaks supersymmetry, while the fermion mass hierarchy results from the wavefunction overlap of bulk fermions with a UV-confined Higgs field. The first and second generation squarks and sleptons, which are localized near the IR brane, directly feel the supersymmetry breaking and obtain masses of order 10 TeV. These are interpreted as composite states of the dual 4D theory.
Continuous Advances in QCD 2008 - Proceedings of the Conference, 2008
We report preliminary results of lattice super-Yang-Mills computations using domain wall fermions... more We report preliminary results of lattice super-Yang-Mills computations using domain wall fermions, performed at an actual rate of 1000 Gflop/s, over the course of six months, using two BlueGene/L racks at Rensselaer's CCNI supercomputing center. This has allowed us to compute the gluino condensate and string tension over a wide range of lattice parameters, setting the stage for continuum, chiral extrapolations. †
The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described ... more The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described in hep-lat/0605003 uses exact lattice chirality to decouple the massless chiral fermions from a mirror sector, whose strong dynamics is conjectured to give cutoff-scale mass to the mirror fermions without breaking the chiral gauge symmetry. In this paper, we study the mirror sector dynamics of a two-dimensional chiral gauge theory in the limit of strong Yukawa and vanishing gauge couplings, in which case it reduces to an XY model coupled to Ginsparg-Wilson fermions. For the mirror fermions to acquire cutoff-scale mass it is believed to be important that the XY model remain in its "high temperature" phase, where there is no algebraic ordering-a conjecture supported by the results of our work. We use analytic and Monte-Carlo methods with dynamical fermions to study the scalar and fermion susceptibilities, and the mirror fermion spectrum. Our results provide convincing evidence that the strong dynamics does not "break" the chiral symmetry (more precisely, that the mirror fermions do not induce algebraic ordering in two-dimensions), and that the mirror fermions decouple from the infrared physics.
We report recent results and developments from our ongoing lattice studies of N = 4 supersymmetri... more We report recent results and developments from our ongoing lattice studies of N = 4 supersymmetric Yang-Mills theory. These include a proof that only a single fine-tuning needs to be performed, so long as the moduli space is not lifted by nonperturbative effects. We extend our investigations of supersymmetry restoration in the continuum limit by initiating Monte Carlo renormalization group studies. We present additional numerical evidence that the lattice theory does not suffer from a sign problem. Finally we study the static potential, which we find to be Coulombic at both weak and strong coupling. We compare the static potential Coulomb coefficients to perturbation theory, including initial results for N = 3 colors in addition to N = 2.
This White Paper has been prepared as a planning document for the Division of High Energy Physics... more This White Paper has been prepared as a planning document for the Division of High Energy Physics of the U. S. Department of Energy. Recent progress in lattice-based studies of physics beyond the standard model is summarized, and major current goals of USQCD research in this area are presented. Challenges and opportunities associated with the recently discovered 126 GeV Higgs-like particle are highlighted. Computational resources needed for reaching important goals are described. The document was finalized on February 11, 2013 with references that are not aimed to be complete, or account for an accurate historical record of the field.
String theories in principle address the origin and values of the quark and lepton masses. Perhap... more String theories in principle address the origin and values of the quark and lepton masses. Perhaps the small values of neutrino masses could be explained generically in string theory even if it is more difficult to calculate individual values, or perhaps some string constructions could be favored by generating small neutrino masses. We examine this issue in the context of the well-known threefamily standard-like Z3 heterotic orbifolds, where the theory is well enough known to construct the corresponding operators allowed by string selection rules, and analyze the D-and F-flatness conditions. Surprisingly, we find that a simple see-saw mechanism does not arise. It is not clear whether this is a property of this construction, or of orbifolds more generally, or of string theory itself. Extended see-saw mechanisms may be allowed; more analysis will be needed to settle that issue. We briefly speculate on their form if allowed and on the possibility of alternatives, such as small Dirac masses and triplet see-saws. The smallness of neutrino masses may be a powerful probe of string constructions in general. We also find further evidence that there are only 20 inequivalent models in this class, which affects the counting of string vacua.
We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the l... more We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U (1) R symmetry is exactly preserved in the limit of vanishing bare mass. We show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.
We show that nonpertubative lattice studies of four-dimensional N =4 Super-Yang-Mills are within ... more We show that nonpertubative lattice studies of four-dimensional N =4 Super-Yang-Mills are within reach. We use Ginsparg-Wilson fermions to avoid gluino masses and an exact implementation of the (chiral) R-symmetry, which greatly limits the number of counterterms that must be fine-tuned. Only bosonic operators require fine tuning, so all tunings can be done "offline" by a Ferrenberg-Swendsen type reweighting. We show what measurables can be used to perform the tuning.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2009
Lattice N = 1 super-Yang-Mills theory formulated using Ginsparg-Wilson fermions provides a rigoro... more Lattice N = 1 super-Yang-Mills theory formulated using Ginsparg-Wilson fermions provides a rigorous non-perturbative definition of the continuum theory that requires no fine-tuning as the lattice spacing is reduced to zero. Domain wall fermions are one explicit scheme for achieving this and using them we have performed large scale Monte Carlo simulations of the theory for gauge group SU (2). We have measured the gaugino condensate, static potential, Creutz ratios and residual mass for several values of the domain wall separation L s , four-dimensional lattice volume, and two values of the bare gauge coupling. With this data we are able to extrapolate the gaugino condensate to the chiral limit, to express it in physical units, and to establish important benchmarks for future studies of super-Yang-Mills on the lattice.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2012
We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fer... more We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, γ = −0.03(13), however taking this source of systematic error into account gives a much larger range of allowed values, −0.6 γ 0.6. We also attempt to measure the anomalous mass dimension using the stability matrix method. We discuss the systematic errors affecting the current analysis and possible improvements.
We present a Monte Carlo Renormalisation Group (MCRG) study of the SU(2) gauge theory with two Di... more We present a Monte Carlo Renormalisation Group (MCRG) study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, gamma=-0.03(13), however without this assumption our uncertainty in the running of the coupling leads to a much larger range of allowed values, -0.6 < gamma < 0.6. We discuss the systematic errors affecting the current analysis and possible improvements.
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Papers by Joel Giedt