Diego Bombardelli

Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal

Moving from the mirror theory Bethe?Yang equations proposed by Arutyunov and Frolov, we derive the thermodynamic Bethe ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence. The associated set of universal functional relations (Y-system) satisfied by the exponentials of the TBA pseudoenergies is deduced, confirming the structure inferred by Gromov, Kazakov and Vieira.

TBA and Y-system for planar AdS(4)/CFT(3)

Abstract 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.

Large spin corrections in N=4 SYM sl(2): Still a linear integral equation

Abstract 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 non-linear 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.

TBA and Y-system for planar

Abstract 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.

Quantum strings and the AdS4/CFT3 interpolating function

The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS4 sector. Several cutoff prescriptions have been proposed, leading to different predictions for the constant term in the expansion

Large spin corrections in

h\left( \lambda \right) = \sqrt {{{{\lambda } \left/ {2} \right.}}} + c + \ldots

{\cal N}=4

. We calculate quantum corrections for giant magnons, using the algebraic curve, and show by comparing to the dispersion relation that the same prescriptions lead to the same values of c in this CP3 sector. We then turn to finite-J effects, where a comparison with the Lüscher F-term correction shows a mismatch for one of the three sum prescriptions. We also compute some dyonic and higher F-terms for future comparisons.

SYM sl(2): still a linear integral equation

Abstract 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 non-linear 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.

An integrability primer for the gauge-gravity correspondence: an introduction

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 re ...

12 loops and triple wrapping in ABJM theory from integrability

A bstractAdapting a method recently proposed by C. Marboe and D. Volin for N=4