Stringy correlations on deformed $Ad{S}_3\times S^3$

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 $Ad{S}_3\times S^3$ 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 $Ad{S}_3$. 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 $Ad{S}_3$ 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.

Typos fixed, Published Version

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• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
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• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
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