标题： 热力学分区函数的$J_3 \bar{J}_3$变形$AdS_3$ 显示英文标题

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

摘要： 我们推导出欧几里得化$J_3 \bar J_3$变形$AdS_3$的一环玻色弦分割函数，作为未变形欧几里得化$AdS_3$分割函数的积分变换，其具有周期性欧几里得时间。这种变形可解释为边界的无关“单迹$T \bar T$变形”。我们将通过首先建立一个形式程序来计算具有精确边缘$J \bar J$变形的σ模型的世界面环面零点函数，该模型具有$U(1)_L \times U(1)_R$全局对称性。然后我们描述该程序如何在$SL(2,R)$σ模型及其欧几里得延续中实现。 最后，我们描述了变形的$SL(2,R)$环面振幅在临界弦理论中的嵌入，并将结果解释为变形理论热力学分区函数的主要微扰贡献。 显示英文摘要

摘要： 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.