A thermodynamic Bethe ansatz for planar AdS/CFT: a proposal

Abstract:We discuss the resummation of the strong coupling asymptotic expansion of the dressing phase of the AdS 5 × S 5 superstring. The dressing phase proposed by Beisert, Eden and Staudacher can be recovered from a modified Borel-Ecalle resummation of this asymptotic expansion only by completing it with new, non-perturbative and exponentially suppressed terms that can be organized into different sectors labelled by an instanton-like number. We compute the contribution to the dressing phase coming from the sum over all the instanton sectors and show that it satisfies the homogeneous crossing symmetry equation. We comment on the semiclassical origin of the non-perturbative terms from the world-sheet theory point of view even though their precise explanation remains still quite mysterious.

Section: Jhep01(2017)055mentioning

confidence: 79%

Resurgence of the dressing phase for AdS5 × S5

Arutyunov

Dorigoni

Savin

2017

“…All these observations should hold for the AdS/CFT Y-systems [7], and in particular for the most studied AdS 5 /CFT 4 case, solving the problem of planar spectrum of anomalous dimensions in N=4 SYM theory (see for the recent review [8], and in particular the chapters [9,10] therein). The AdS 5 /CFT 4 Y-and T-systems with T-hook boundary conditions proposed in [7] and summarized in figure 1 were later shown to be equivalent, with certain analyticity requirements [11][12][13], to the TBA equations [14][15][16]. It was shown in [17,18] (see also [19,20]) that the T-system, and hence the Y-system, in T-hook can be formally solved in terms of Wronskian determinants of a finite number of Q-functions -a generalization of Baxter's Q-function.…”

Section: Jhep07(2012)023mentioning

confidence: 95%

“…2 In addition to the shape of the pa, sq domain one should also specify the analyticity properties of the Y-functions. These properties can be deduced from the TBA equations [14][15][16] and were explicitly written in [9,11,13].…”

Section: Ads/cft Y-systemmentioning

confidence: 99%

Solving the AdS/CFT Y-system

Gromov

Казаков

Leurent³

et al. 2012

297

Using integrability and analyticity properties of the AdS 5 /CFT 4 Y-system we reduce it to a finite set of nonlinear integral equations. The Z 4 symmetry of the underlying coset sigma model, in its quantum version, allows for a deeper insight into the analyticity structure of the corresponding Y-functions and T-functions, as well as for their analyticity friendly parameterization in terms of Wronskian determinants of Q-functions. As a check for the new equations, we reproduce the numerical results for the Konishi operator previously obtained from the original infinite Y-system.

“…Based on the experience that integrability techniques usually start with a large-volume limit, this would probably require the adaption of a full thermodynamic Bethe ansatz [44][45][46][47][48] or quantum spectral curve [49] machinery.…”

Section: Jhep03(2014)096mentioning

confidence: 99%

Computing three-point functions for short operators

Bargheer

Minahan

Pereira

2014

Abstract:We compute the three-point structure constants for short primary operators of N = 4 super Yang-Mills theory to leading order in 1/ √ λ by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.