Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT

TL;DR

This paper explores nonlocal symmetries in symmetric space models related to AdS/CFT, focusing on a master symmetry that generates spectral parameters and deforms minimal surfaces, revealing new algebraic structures and applications.

Contribution

It introduces a master symmetry generating spectral parameters in AdS/CFT, extending to an infinite symmetry tower with conserved charges, and provides a numerical framework for minimal surface deformations.

Findings

Identification of a master symmetry generating spectral parameters.

Establishment of an infinite tower of nonlocal symmetries.

Development of a numerical method for minimal surface deformation.

Abstract

We give a general account of nonlocal symmetries in symmetric space models and their relation to the AdS/CFT correspondence. In particular, we study a master symmetry which generates the spectral parameter and acts as a level-raising operator on the classical Yangian generators. The master symmetry extends to an infinite tower of symmetries with nonlocal Casimir elements as associated conserved charges. We discuss the algebraic properties of these symmetries and establish their role in explaining the recently observed one-parameter deformation of holographic Wilson loops. Finally, we provide a numerical framework, in which discretized minimal surfaces and their master symmetry deformation can be calculated.