Matrix model correlators from non-Abelian T-dual of $AdS_5 \times S^5 $

TL;DR

This paper investigates scalar and vector perturbations in the non-Abelian T-dual of $AdS_5 imes S^5$, establishing a holographic dictionary for scalar operators in a dual matrix model and analyzing their correlation functions.

Contribution

It provides the first detailed holographic analysis of scalar and vector perturbations in the non-Abelian T-dual of $AdS_5 imes S^5$, linking bulk modes to dual matrix model operators.

Findings

Scalar operators are marginal or irrelevant deformations at strong coupling.

Calculated two-point correlation functions for scalar operators.

Derived boundary charge density at finite chemical potential.

Abstract

We study various perturbations and their holographic interpretation for non-Abelian T-dual of $ AdS_5 \times S^5 $ where the T-duality is applied along the $ SU(2) $ of $ AdS_5 $. This paper focuses on two types of perturbations, namely the scalar and the vector fields on NATD of $ AdS_5 \times S^5 $. For scalar perturbations, the corresponding solutions could be categorised into two classes. For one of these classes of solutions, we build up the associated holographic dictionary where the asymptotic radial mode sources scalar operators for the $ (0+1) $d matrix model. These scalar operators correspond to either a marginal or an irrelevant deformation of the dual matrix model at strong coupling. We calculate the two point correlation between these scalar operators and explore their high as well as low frequency behaviour. We also discuss the completion of these geometries by setting an upper cut-off along the holographic axis and discuss the corresponding corrections to the scalar correlators in the dual matrix model. Finally, we extend our results for vector perturbations where we obtain asymptotic solutions for a particular class of modes. These are further used to calculate the boundary charge density at finite chemical potential.