论文标题
精确$ t \ bar {t} $ - 在球体上的二维杨米尔斯理论的变形
Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere
论文作者
论文摘要
我们通过在其Instanton表示的级别上进行分析来研究零属的二维Yang-Mills理论的$ t \ bar {t} $变形。我们首先要考虑其在变形参数$μ$中的功率扩展来关注扰动部门。通过通过复活理论研究所得的渐近系列，我们确定了输入$μ<0 $的结果的非扰动贡献。然后，我们通过求解相关的流程方程将此分析扩展到任何通量扇区。具体而言，我们施加了对应于两个不同方案的边界条件：量子未呈现的理论和变形理论的半经典极限。完整的分区函数作为总和在所有磁通量上获得。对于任何$μ> 0 $，只有有限的量子频谱存活，分区函数可在有限的一组表示方面减少到总和。对于$μ<0 $，通过产生非平凡减法的有趣机制将分区函数正常化。
We study the $T\bar{T}$ deformation of two-dimensional Yang-Mills theory at genus zero by carrying out the analysis at the level of its instanton representation. We first focus on the perturbative sector by considering its power expansion in the deformation parameter $μ$. By studying the resulting asymptotic series through resurgence theory, we determine the nonperturbative contributions that enter the result for $μ<0$. We then extend this analysis to any flux sector by solving the relevant flow equation. Specifically, we impose boundary conditions corresponding to two distinct regimes: the quantum undeformed theory and the semiclassical limit of the deformed theory. The full partition function is obtained as a sum over all magnetic fluxes. For any $μ>0$, only a finite portion of the quantum spectrum survives and the partition function reduces to a sum over a finite set of representations. For $μ<0$, nonperturbative contributions regularize the partition function through an intriguing mechanism that generates nontrivial subtractions.
