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arXiv · 2403.03979

Thermal partition function of $J_3 \bar{J}_3$ deformed $AdS_3$

Soumangsu Chakraborty·Amit Giveon·Akikazu Hashimoto
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Abstract

We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized $J_3 \bar J_3$ deformed $AdS_3$ with periodic Euclidean time as an integral transform of the partition function of the undeformed Euclideanized $AdS_3$. Such a deformation is interpretable as an irrelevant "single-trace $T \bar T$ deformation" of the boundary. We will do this by first establishing a formal procedure to compute a worldsheet torus zero point function for an exactly marginal $J \bar J$ deformation of a sigma model with $U(1)_L \times U(1)_R$ global symmetry. We then describe how this procedure is implemented on $SL(2,R)$ sigma model and its Euclidean continuation. Finally, we describe the embedding of the deformed $SL(2,R)$ torus amplitude into critical string theory and interpret the result as the leading perturbative contribution to the thermal partition function of the deformed theory.

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Soumangsu Chakraborty, Amit Giveon, Akikazu Hashimoto. 2024-03-06. Thermal partition function of $J_3 \bar{J}_3$ deformed $AdS_3$. https://arxiv.org/abs/2403.03979

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