Papers by Diego Bombardelli
arXiv (Cornell University), Jun 30, 2015
Adapting a method recently proposed by C. Marboe and D. Volin for N =4 super-Yang-Mills, we devel... more Adapting a method recently proposed by C. Marboe and D. Volin for N =4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the sl(2)-like sector of planar N =6 super-Chern-Simons. The method relies on the Quantum Spectral Curve formulation of the problem and the expansion is written in terms of the interpolating function h(λ), with coefficients expressible as combinations of Euler-Zagier sums with alternating signs. We present explicit results up to 12 loops (six nontrivial orders) for various twist-1 and twist-2 operators, corresponding to triple and double wrapping terms, respectively, which are beyond the reach of the Asymptotic Bethe Ansatz as well as Lüscher's corrections. The algorithm works for generic states in this sector and in principle can be used to compute arbitrary orders of the weak coupling expansion. For the simplest operator with L=1 and spin S=1, the Padé extrapolation of the 12-loop result nicely agrees with the available Thermodynamic Bethe Ansatz data in a relatively wide range of values of the coupling. A Mathematica notebook with a selection of results is attached.
Nuclear Physics B, 2010
We conjecture the set of asymptotic Bethe Ansatz equations for the mirror model of the AdS 4 ×CP ... more We conjecture the set of asymptotic Bethe Ansatz equations for the mirror model of the AdS 4 ×CP 3 string theory, corresponding to the planar N = 6 superconformal Chern-Simons gauge theory in three dimensions. Hence, we derive the (vacuum energy) thermodynamic Bethe Ansatz equations and the Y-system describing the direct AdS 4 /CFT 3 string theory.
In this thesis, we present our work about some generalisations of ideas, techniques and physical ... more In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoerie...
Journal of Physics A: Mathematical and Theoretical, 2016
In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mai... more In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU (2), SU (3) chiral Gross-Neveu models. This is part of a collection of lecture notes for the Young Researchers Integrability School, organized by the GATIS network at Durham University on 6-10 July 2015.
Journal of High Energy Physics, 2014
We propose a next-to-leading Lüscher-like formula for the finite-size corrections of the excited ... more We propose a next-to-leading Lüscher-like formula for the finite-size corrections of the excited states energies in integrable theories. We conjecture the expressions of the corrections for both the energy and the particles' rapidities by interpreting the excited states as momenta-dependent defects. We check the resulting formulas in some simple relativistic model and conjecture those for the AdS 5 /CF T 4 case.
Physical Review D, 2005
We study cosmology in the five-dimensional Randall-Sundrum brane-world with a stabilizing effecti... more We study cosmology in the five-dimensional Randall-Sundrum brane-world with a stabilizing effective potential for the radion and matter localized on the branes. The analysis is performed by employing a perturbative expansion in the ratio ρ/V between the matter energy density on the branes and the brane tensions around the static Randall-Sundrum solution (which has ρ = 0 and brane tensions ±V). This approach ensures that the matter evolves adiabatically and allows us to find approximate solutions to second order in ρ/V. Some particular cases are then analyzed in details.
Journal of Physics A: Mathematical and Theoretical, 2012
arXiv: High Energy Physics - Theory, 2007
We survey and discuss the applications of the non-linear integral equation in the framework of th... more We survey and discuss the applications of the non-linear integral equation in the framework of the Bethe Ansatz type equations which are conjectured to give the eigenvalues of the dilatation operator in N = 4 SYM. Moreover, an original idea (different from that of [1]) to derive a non-linear integral equation is briefly depicted in Section 4.
Journal of High Energy Physics, 2018
The Quantum Spectral Curve (QSC) equations for planar $$ \mathcal{N}=6 $$ N = 6 super-conformal C... more The Quantum Spectral Curve (QSC) equations for planar $$ \mathcal{N}=6 $$ N = 6 super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the $$ \mathfrak{s}\mathfrak{l}\left(2\Big|1\right) $$ s l 2 | 1 sector. New weak coupling results for conformal dimensions of operators outside the $$ \mathfrak{s}\mathfrak{l}(2) $$ s l 2 -like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator 20 is ruled out by our analysis. The results of this ...
Journal of High Energy Physics, 2017
The spectrum of planar N = 6 superconformal Chern-Simons theory, dual to type IIA superstring the... more The spectrum of planar N = 6 superconformal Chern-Simons theory, dual to type IIA superstring theory on AdS 4 × CP 3 , is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in depth the basic integrability structure underlying the spectral problem, the Quantum Spectral Curve. The new results presented in this paper open the way to the quantitative study of the spectrum for arbitrary operators at finite coupling. Besides, we show that the Quantum Spectral Curve is embedded into a novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and leads to exact Bethe Ansatz equations. The discovery of this algebraic structure, more intricate than the one appearing in the AdS 5 /CFT 4 case, could be a first step towards the extension of the method to AdS 3 /CFT 2 .
Journal of High Energy Physics, 2018
We investigate low-energy string excitations in AdS3 × S3 × T4. When the worldsheet is decompacti... more We investigate low-energy string excitations in AdS3 × S3 × T4. When the worldsheet is decompactified, the theory has gapless modes whose spectrum at low energies is determined by massless relativistic integrable S matrices of the type introduced by Al. B. Zamolodchikov. The S matrices are non-trivial only for excitations with identical worldsheet chirality, indicating that the low-energy theory is a CFT2. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes’ wrapping effects may be incorporated into the AdS3 spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low-energy CFT2 to be c = 6 from calculating the vacuum energy for antiperiodic fermions — with the vacuum energy being zero for periodic fermions in agreement with a supersymmetric theory — and find the energies of some excited states.
Journal of Physics A: Mathematical and Theoretical, 2016
We introduce a series of articles reviewing various aspects of integrable models relevant to the ... more We introduce a series of articles reviewing various aspects of integrable models relevant to the anti-de Sitter (AdS)/conformal quantum field theory (CFT) correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in (conformal) quantum field theory. In the present article we highlight how these concepts have found application in AdS/CFT, and provide a brief overview of the material contained in this series.
Phys Lett B, 2010
We propose that certain twists of the su(2|2) S-matrix elements describe the β-deformation of N =... more We propose that certain twists of the su(2|2) S-matrix elements describe the β-deformation of N = 4 supersymmetric Yang-Mills theory. We compute the perturbative four-loop anomalous dimension of the Konishi operator of the deformed gauge theory from the Lüscher formula based on these twisted S-matrix elements. The result agrees exactly with the perturbative gauge theory computations.
Journal of High Energy Physics, 2015
Adapting a method recently proposed by C. Marboe and D. Volin for N =4 super-Yang-Mills, we devel... more Adapting a method recently proposed by C. Marboe and D. Volin for N =4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the sl(2)-like sector of planar N =6 super-Chern-Simons. The method relies on the Quantum Spectral Curve formulation of the problem and the expansion is written in terms of the interpolating function h(λ), with coefficients expressible as combinations of Euler-Zagier sums with alternating signs. We present explicit results up to 12 loops (six nontrivial orders) for various twist-1 and twist-2 operators, corresponding to triple and double wrapping terms, respectively, which are beyond the reach of the Asymptotic Bethe Ansatz as well as Lüscher's corrections. The algorithm works for generic states in this sector and in principle can be used to compute arbitrary orders of the weak coupling expansion. For the simplest operator with L=1 and spin S=1, the Padé extrapolation of the 12-loop result nicely agrees with the available Thermodynamic Bethe Ansatz data in a relatively wide range of values of the coupling. A Mathematica notebook with a selection of results is attached.
Journal of High Energy Physics, 2011
The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive th... more The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive the leading and next-to-leading order (NLO) Lüscher-type corrections for large volumes of the vacuum energy for integrable theories with twisted boundary conditions and twisted S-matrix. We then derive the twisted thermodynamic Bethe ansatz (TBA) equations to describe exactly the ground state, from which we obtain an untwisted Y-system. The two approaches are compared by expanding the TBA equations to NLO, and exact agreement is found. We give explicit results for the O(4) model and for the three-parameter family of γ-deformed (non-supersymmetric) planar AdS/CFT model, where the ground-state energy can be nontrivial and can acquire finite-size corrections. The NLO corrections, which correspond to double-wrapping diagrams, are explicitly evaluated for the latter model at six loops.
Journal of High Energy Physics, 2010
Journal of High Energy Physics, 2009
We compute classical and first quantum finite-size corrections to the recently found giant magnon... more We compute classical and first quantum finite-size corrections to the recently found giant magnon solutions in two different subspaces of CP 3. We use the Lüscher approach on the recently proposed exact S-matrix for N = 6 superconformal Chern-Simons theory. We compare our results with the string and algebraic curve computations and find agreement, thus providing a non-trivial test for the new AdS 4 /CF T 3 correspondence within an integrability framework. 2 See also [12] for the original derivation of the SYM Bethe Ansatz equations from the AdS 5 /CF T 4 S-matrix 3 We ought to thank G. Grignani for clarifying this point to us.
Physics Letters B, 2012
We compute both classical and quantum finite-size corrections at leading order in the strong coup... more We compute both classical and quantum finite-size corrections at leading order in the strong coupling limit for the (dyonic) giant magnon in the Lunin-Maldacena background. Based on the exact S-martix conjectured for the deformed theory, we generalize the Lüscher formula to include twisted boundary conditions and show that the results match with those derived both by finite-size classical solutions of the giant magnon and by algebraic curve analysis.
Nuclear Physics B, 2009
Anomalous dimension and higher conserved charges in the sl(2) sector of N = 4 SYM for generic spi... more Anomalous dimension and higher conserved charges in the sl(2) sector of N = 4 SYM for generic spin s and twist L are described by using a novel kind of nonlinear integral equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-linear (finite range) integral terms, appearing in the NLIE and in the dimension formula, go to zero as s → ∞. Therefore they can be neglected at least up to the O(s 0) order, thus implying a linear integral equation (LIE) and a linear dimension/charge formula respectively, likewise the 'thermodynamic' (i.e. infinite spin) case. Importantly, these non-linear terms go faster than any inverse logarithm power (ln s) −n , n > 0, thus extending the linearity validity.
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Papers by Diego Bombardelli