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arXiv 2009.00657hep-thmath-phmath.MPmath.QA
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$q$-Yang-Mills理论的$T\overline{T}$-形变

$T\overline{T}$-deformation of $q$-Yang-Mills theory

Leonardo Santilli, Richard J. Szabo, Miguel Tierz

备注：
43 pages, 12 figures; v2: typos corrected, references added; v3: minor corrections; Final version published in JHEP
发表信息：
J. High Energ. Phys. 2020, 86 (2020)
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AI总结：

本文利用Jackiw-Teitelboim引力构造任意黎曼曲面上$q$-Yang-Mills理论的$T\overline{T}$形变，分析其大$N$相变、因式分解破裂与纠缠熵变化。

摘要：

我们通过将一阶形式体系中的未扰动理论与Jackiw-Teitelboim引力耦合，在任意黎曼曲面上导出了二维$q$-形变Yang-Mills理论的$T\overline{T}$-扰动版本。我们表明，$T\overline{T}$-形变导致其与Seifert流形上Chern-Simons理论之间联系的破裂，也导致大$N$下分解为手征与反手征部分的因式分解失效。对于球面上的$U(N)$规范理论，我们证明大$N$相变仍然存在，并且该相变为三阶、由瞬子诱导。$T\overline{T}$-形变的作用是降低't Hooft耦合的临界值，同时扩大发生相变的线丛类别。相同结果被证明适用于$(q,t)$-形变Yang-Mills理论。我们还在Yang-Mills理论的大$N$极限中显式计算了纠缠熵，表明$T\overline{T}$-形变降低了Boltzmann熵的贡献。

英文摘要：

We derive the $T\overline{T}$-perturbed version of two-dimensional $q$-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $T\overline{T}$-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large $N$ factorization into chiral and anti-chiral sectors. For the $U(N)$ gauge theory on the sphere, we show that the large $N$ phase transition persists, and that it is of third order and induced by instantons. The effect of the $T\overline{T}$-deformation is to decrease the critical value of the 't Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for $(q,t)$-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large $N$ limit of Yang-Mills theory, showing that the $T\overline{T}$-deformation decreases the contribution of the Boltzmann entropy.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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