Some comments on spacelike minimal surfaces with null polygonal boundaries in AdS m

154

256

We compute N = 4 Super Yang Mills planar amplitudes at strong coupling by considering minimal surfaces in AdS 5 space. The surfaces end on a null polygonal contour at the boundary of AdS. We show how to compute the area of the surfaces as a function of the conformal cross ratios characterizing the polygon at the boundary. We reduce the problem to a simple set of functional equations for the cross ratios as functions of the spectral parameter. These equations have the form of Thermodynamic Bethe Ansatz equations. The area is the free energy of the TBA system. We consider any number of gluons and in any kinematic configuration.

Section: The Classical Sigma Model and Hitchin Equationsmentioning

confidence: 99%

Section: Integrable Theories With Virasoro Constraints and Hitchin's mentioning

confidence: 99%

Y-system for scattering amplitudes

Alday

Maldacena

Sever

et al. 2010

154

256

“…one finds precisely the set of equations (A.8), (A.9) and (A.10) that arise in the coordinate formulation of the Pohlmeyer reduction of strings moving in AdS space (see, e.g., [46,52,53] and appendix A).…”

Section: Expanding These Equations In Componentsmentioning

confidence: 98%

“…Therefore, to construct such actions in this Pohlmeyer reduction for space-like world-sheets alternative gauge-fixings need to be used. However, in general it should be possible to find such gauge-fixings achieving the same effect as the imaginary rotations of the fields β, U , V and X described above (see, for example[53,55]).…”

mentioning

confidence: 96%

Pohlmeyer reduction for superstrings in AdS space

Hoare¹,

Tseytlin²

2012

The Pohlmeyer reduced equations for strings moving only in the AdS subspace of AdS5 × S 5 have been used recently in the study of classical Euclidean minimal surfaces for Wilson loops and some semiclassical three-point correlation functions. We find an action that leads to these reduced superstring equations. For example, for a bosonic string in AdSn such an action contains a Liouville scalar part plus a K/K gauged WZW model for the group K = SO(n − 2) coupled to another term depending on two additional fields transforming as vectors under K. Solving for the latter fields gives a non-abelian Toda model coupled to the Liouville theory. For n = 5 we generalize this bosonic action to include the S 5 contribution and fermionic terms. The corresponding reduced model for the AdS2 × S 2 truncation of the full AdS5 × S 5 superstring turns out to be equivalent to N = 2 super Liouville theory. Our construction is based on taking a limit of the previously found reduced theory actions for bosonic strings in AdSn × S 1 and superstrings in AdS5 × S 5 . This new action may be useful as a starting point for possible quantum generalizations or deformations of the classical Pohlmeyer-reduced theory. We give examples of simple extrema of this reduced superstring action which represent strings moving in the AdS5 part of the space. Expanding near these backgrounds we compute the corresponding fluctuation spectra and show that they match the spectra found in the original superstring theory.

“…are rather easily connected with (136) [75][76][77]. The area A of the worldsheet is then computed thanks to the metric g as follows…”

Section: Minimal Surfaces In Adsmentioning

confidence: 99%

Geometric aspects of the ODE/IM correspondence

Dorey¹,

Dunning²,

Negro³

et al. 2020

This review describes a link between Lax operators, embedded surfaces and Thermodynamic Bethe Ansatz equations for integrable quantum field theories. This surprising connection between classical and quantum models is undoubtedly one of the most striking discoveries that emerged from the o -critical generalisation of the ODE/IM correspondence, which initially involved only conformal invariant quantum field theories. We will mainly focus of the KdV and sinh-Gordon models. However, various aspects of other interesting systems, such as a ne Toda field theories and non-linear sigma models, will be mentioned. We also discuss the implications of these ideas in the AdS/CFT context, involving minimal surfaces and Wilson loops. This work is a follow-up of the ODE/IM review published more than ten years ago by JPA, before the discovery of its o -critical generalisation and the corresponding geometrical interpretation.(Partially based on lectures given at the "Young Researchers Integrability School 2017", in Dublin.) 1 arXiv:1911.13290v2 [hep-th]