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

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.