Stability and boundedness in AdS/CFT with double trace deformations II: Vector Fields

TL;DR

This paper investigates the stability and boundedness of vector fields in AdS/CFT with double trace deformations, revealing distinct algebraic structures and analyzing physical properties at finite temperature.

Contribution

It extends previous scalar field analysis to vector fields, identifying differences between two types of double trace deformations and exploring their physical implications.

Findings

Double trace deformation of Marolf and Ross yields an SL(2,R) family of theories.

Double trace deformation of Witten results in an independent SL(2,Z) structure.

Finite temperature two-point functions reveal susceptibility and low-lying spectrum features.

Abstract

We extend the analysis of boundedness and stability, initiated for scalar fields in anti de Sitter space in a previous work, to the case of vector fields. We show that the double trace deformation of Marolf and Ross is distinct from the double trace deformation of Witten. The former gives rise to an $SL(2,{\bf R})$ family of theories whereas the latter gives rise to an independent $SL(2,{\bf Z})$. We analyze the finite temperature two-point correlation function of current operators and infer the susceptibility and spectrum of low lying states. We discuss various physical features exhibited by these theories.