# Stringy correlations on deformed $ AdS_{3}\times S^{3} $

## TL;DR

This paper investigates how stringy correlations in a deformed $AdS_3 imes S^3$ background decay with distance, revealing exponential suppression at small deformations and saturation at large deformations, using strong coupling calculations.

## Contribution

It provides a strong coupling analysis of two-point functions in a $"kappa$-deformed $AdS_3 imes S^3$ background, including finite size corrections and behavior under varying deformation strength.

## Key findings

- Exponential decay of two-point functions at small deformations.
- Saturation of two-point functions at large deformations.
- Agreement with previous results at zero deformation.

## Abstract

In this paper, following the basic prescriptions of Gauge/String duality, we perform a strong coupling computation on \textit{classical} two point correlation between \textit{local} (single trace) operators in a gauge theory dual to $ \kappa $-deformed $ AdS_{3}\times S^{3}$ background. Our construction is based on the prescription that relates every local operator in a gauge theory to that with the (semi)classical string states propagating within the \textit{physical} region surrounded by the holographic screen in deformed $ AdS_3 $. In our analysis, we treat strings as being that of a point like object located near the physical boundary of the $ \kappa $- deformed Euclidean Poincare $ AdS_{3} $ and as an extended object with non trivial dynamics associated to $ S^{3} $. It turns out that in the presence of small background deformations, the usual power law behavior associated with two point functions is suppressed exponentially by a non trivial factor which indicates a faster decay of two point correlations with larger separations. On the other hand, in the limit of large background deformations ($ \kappa \gg 1 $), the corresponding two point function reaches a point of saturation. In our analysis, we also compute finite size corrections associated with these two point functions at strong coupling. As a consistency check of our analysis, we find perfect agreement between our results to that with the earlier observations made in the context of vanishing deformation.