arXiv 2207.050952022-07-11hep-th

球面上二维Yang-Mills理论的精确$T\bar{T}$ -形变

Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere

Luca Griguolo, Rodolfo Panerai, Jacopo Papalini, Domenico Seminara

备注：: 36 pages, 4 figures
DOI：: 10.1007/JHEP10(2022)134

摘要：

通过在瞬子表象水平上的分析，研究了亏格为零的二维Yang-Mills理论的$T\bar{T}$形变.首先，我们专注于微扰部门考虑其权力膨胀的变形参数$μ$。通过研究由此产生的渐近级数通过复苏理论，我们确定的非微扰的贡献，进入结果$μ<0$。然后，我们将此分析扩展到任何通量部门解决相关的流量方程。具体来说，我们施加边界条件对应于两个不同的制度：量子未变形理论和变形理论的半经典极限。完整的配分函数作为所有磁通量的总和而获得。对于任何$μ>0$，只有有限部分的量子谱存活，并且配分函数减少到有限表示集上的和。对于$μ<0$，非微扰贡献通过产生非平凡减法的有趣机制来正则化配分函数。

英文摘要：

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.

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摘要：

英文摘要：

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