Y-system for γ-deformed ABJM theory

Abstract

We investigate the integrable aspects of the planar γ-deformed ABJM theory and propose the twisted asymptotic Bethe ansatz equations. A more general method through a twisted generating functional is discussed, based on which, the asymptotic large L solution of Y-system is modified in order to match the asymptotic Bethe ansatz equations. Several applications of our method in the sl(2)-like sector and some important examples in β-deformed ABJM are presented as well.

Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models

“…Besides, other variants of the SYK model have been investigated not only in high energy physics, but also in condensed matter physics [18][19][20][21][22][23][24][25][26][27][28][29][30][31] because of its relevance to non-Fermi liquid, the quantum critical phenomena, and the effect of disorder in strongly correlated systems. For example, there are many extensions of the SYK model: that with q-point interactions [4], that with hard-core bosons [19], SUSY extensions [32][33][34][35][36][37], disorder-free tensor models [35,38], the SYK model with a lattice structure [24,25,[39][40][41][42], and a kind of coupled or perturbed system [23,26,27,[29][30][31]. Furthermore, experimental implementation of the SYK model has been theoretically proposed with ultracold atoms and solid-state devices [20][21][22].…”

RG stability of integrable fishnet models

“…Recently, several efforts have been devoted to the characterization of the integrabilitypreserving continuous deformations of these maximally supersymmetric models [5][6][7][8][9], usually called γ-deformations in the literature. These type of deformations can be implemented in the holographic setting using a sequence of up to three independent T-duality, shift, Tduality (TsT) transformations.…”

Finite-size effect for dyonic giant magnons inCPβ3

“…This is a three-parameter deformation which breaks supersymmetry completely, while here we are interested in the β-deformed theory with γ 1 = γ 2 = 0, γ 3 = β which preserves N = 2 supersymmetry. 1 In our recent paper [15], the integrable structure of γ-deformed ABJM theory was investigated in detail. The twist matrices were obtained in various bases.…”

“…In this paper, we will try to calculate the finite-size effect for giant magnons in AdS 4 × CP 3 β using classical spectral curve. In order to compare our results with [2], we had better to use different charges from our previous choice in [15]. These charges are listed in Table 1.…”

“…2 γ-deformed ABA at strong coupling In this section we briefly review the γ-deformed AdS 4 /CFT 3 asymptotic Bethe ansatz(ABA) equations and introduce some notations which will be useful in the following sections. In this section, we use the same notation as our previous paper [15]. Let's first define some useful functions as…”