论文标题
$ t \ bar {t}/j \ bar {t} $ - 从Chern-Simons ADS $ _3 $重力带有混合边界条件的变形WZW模型
$T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS$_3$ gravity with mixed boundary conditions
论文作者
论文摘要
在这项工作中，我们认为ADS $ _3 $引力理论具有空间无穷大的某些混合边界条件。使用ADS $ _3 $重力的Chern-Simons形式主义，我们发现这些边界条件导致了非平凡的边界条件，进而使$ t \ bar {t}/j \ bar {t} $ - 变形的CFT产生$ t \ bar {t}/j \ bar {t}/j \ bar {t}/j。然后，我们遵循构造AD $ _3 $的渐近边界动力学的过程，以得出Chern-Simons Gravity的约束$ t \ bar {t} $ - 变形的WZW模型。结果理论证明是$ t \ bar {t} $ - 在解散约束后变形的Alekseev-Shatashvili动作。此外，通过添加与当前$ j $相关的$ u（1）$量规字段，我们获得了一种类型的$ j \ bar t $ t $变形的WZW型号，并证明其动作可以从重力方构建。这些结果提供了$ t \ bar {t}/j \ bar {t} $ - 变形的CFT和ADS $ _3 $的边界条件的变形之间的对应关系，后者可以被视为坐标变换。
In this work we consider AdS$_3$ gravitational theory with certain mixed boundary conditions at spatial infinity. Using the Chern-Simons formalism of AdS$_3$ gravity, we find that these boundary conditions lead to non-trivial boundary terms, which, in turn, produce exactly the spectrum of the $T\bar{T}/J\bar{T}$-deformed CFTs. We then follow the procedure for constructing asymptotic boundary dynamics of AdS$_3$ to derive the constrained $T\bar{T}$-deformed WZW model from Chern-Simons gravity. The resulting theory turns out to be the $T\bar{T}$-deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a $U(1)$ gauge field associated to the current $J$, we obtain one type of the $J\bar T$-deformed WZW model, and show that its action can be constructed from the gravity side. These results provide a check on the correspondence between the $T\bar{T}/J\bar{T}$-deformed CFTs and the deformations of boundary conditions of AdS$_3$, the latter of which may be regarded as coordinate transformations.
