Integrable λ-deformations: squashing coset CFTs and AdS5 × S5

Saskia Demulder,Konstantinos Sfetsos,Daniel C. Thompson

doi:10.1007/jhep07(2015)019

Saskia Demulder, Konstantinos Sfetsos + Show 1 more

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https://doi.org/10.1007/jhep07(2015)019

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Abstract

We examine integrable λ-deformations of SO(n + 1)/SO(n) coset CFTs and their analytic continuations. We provide an interpretation of the deformation as a squashing of the corresponding coset σ-model’s target space. We realise the λ-deformation for n = 5 case as a solution to supergravity supported by non-vanishing five-form and dilaton. This interpolates between the coset CFT SO(4, 2)/SO(4, 1) × SO(6)/SO(5) constructed as a gauged WZW model and the non-Abelian T-dual of the AdS5 × S5 spacetime.

Highlights

We examine integrable λ-deformations of SO(n + 1)/SO(n) coset CFTs and their analytic continuations
A very natural question we are led to ask is if we can relax some of the assumptions of supersymmetry whilst preserving integrability? One reason to hope this is possible is that it is known even QCD itself exhibits some integrability in certain limits [7, 8]
N = 4 Yang-Mills theory admits a class of marginal deformations contained with those of [9], known as β-deformations, that modify the superpotential, preserve only the minimal amount of supersymmetry but yet preserve integrability

Summary

Introduction

A very natural question we are led to ask is if we can relax some of the assumptions of supersymmetry whilst preserving integrability? One reason to hope this is possible is that it is known even QCD itself exhibits some integrability in certain limits [7, 8]. The η-deformations were introduced by Delduc, Magro and Vicedo in [15, 16] and are based on Yang-Baxter σ-models proposed by Klimcik [17] These are described by σ-models propagating in a spacetime that is deformed from the original AdS5 × S5 in a way that preserves no supersymmetries and only an Abelian isometry group. Despite this reduced symmetry, this deformation does preserve classical integrability of the σ-model. The Lax pair formulation for λ-deformations based on symmetric spaces has been explicitly given in [24] In this case, the deformation is driven by parafermion bilinears which are the natural object with definite chirality on shell. Deformations of specific coset cases will be considered in detail in this paper and in particular we will focus on the coset SO(n + 1)/SO(n) and its analytic continuations

Objectives

Conclusion