论文标题
2D和连续$ \ sqrt {t \ bar {t}} $变形的共形代数的非线性自动形态
Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
论文作者
论文摘要
2D（diff（$ s^{1} $）$ \ oplus $ diff（$ s^{1} $））中的共形代数显示在与chiral（holomorphic）生成器$ t $ t $和$ \ bar {t} $的非线性映射下保留。它取决于一个真实参数，可以将其视为``非线性$ so（1,1）$自动形态''。反过来，可以分析以封闭形式分析求解变形作用的相应流动方程的一般解，从而恢复非线性自动构造。变形的CFT $ _ {2} $也可以通过原始理论对磁场依赖的弯曲度量进行描述，该曲线的弯曲和移位函数分别由变形的Hamiltonian相对于能量和动量密度的变化给出。然后，也可以看到，变形理论的共形对称性是由差异形态形成而产生的，这些差异形态可实现适当变形的保形杀伤方程。此外，在非线性自动形态下，表明Cardy公式可将其映射到ITSEFT。作为一个简单的例子，简要解决了$ n $ boto玻色子的变形，与最近的相关结果和Modmax理论的尺寸降低接触。此外，在2D中的保形代数之间的非线性图及其超/非相关版本（bms $ _ {3} $ _ {3} $ cca $ _ {2} $ _ {2} $ gca $ _ $ gca $ _ {2} $，包括相应的有限$ \ sqrt}非线性自动形态的限制情况。还简要讨论了保形代数的三参数非线性ISO（1,1）$自动形态，以及BMS $ _ {3} $的离散非线性自动形态的扩展。
The conformal algebra in 2D (Diff($S^{1}$)$\oplus$Diff($S^{1}$)) is shown to be preserved under a nonlinear map that mixes both chiral (holomorphic) generators $T$ and $\bar{T}$. It depends on a single real parameter and it can be regarded as a ``nonlinear $SO(1,1)$ automorphism.'' The map preserves the form of the momentum density and naturally induces a flow on the energy density by a marginal $\sqrt{T\bar{T}}$ deformation. In turn, the general solution of the corresponding flow equation of the deformed action can be analytically solved in closed form, recovering the nonlinear automorphism. The deformed CFT$_{2}$ can also be described through the original theory on a field-dependent curved metric whose lapse and shift functions are given by the variation of the deformed Hamiltonian with respect to the energy and momentum densities, respectively. The conformal symmetries of the deformed theories can then also be seen to arise from diffeomorphisms that fulfill suitably deformed conformal Killing equations. Besides, Cardy formula is shown to map to itseft under the nonlinear automorphism. As a simple example, the deformation of $N$ free bosons is briefly addressed, making contact with recent related results and the dimensional reduction of the ModMax theory. Furthermore, the nonlinear map between the conformal algebra in 2D and its ultra/non-relativistic versions (BMS$_{3}$$\approx$CCA$_{2}$$\approx$GCA$_{2}$), including the corresponding finite $\sqrt{T\bar{T}}$ deformation, are recovered from a limiting case of the nonlinear automorphism. The extension to a three-parameter nonlinear $ISO(1,1)$ automorphism of the conformal algebra, and a discrete nonlinear automorphism of BMS$_{3}$ are also briefly discussed.
