Modified instanton sum in QCD and higher-groups
Modified instanton sum in QCD and higher-groups
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DOI：
10.1007/jhep03(2020)123
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发表时间：
2019-12
影响因子：
5.4
通讯作者：
Y. Tanizaki;M. Ünsal
中科院分区：
文献类型：
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作者：
Y. Tanizaki;M. Ünsal
我们考虑SU（N）Yang-Mills理论，它的拓扑扇区被限制在p的整数倍的瞬子数，我们可以建立这样一个保持定域性和么正性的量子场论，并且该模型包含2π周期标量场和3形式规范场.这可以解释为将一个拓扑理论耦合到杨-米尔斯理论上，从而使局部动力学与纯杨-米尔斯理论完全一致。该理论不仅具有π N 1-形式对称性，而且具有π p 3-形式对称性，并从最近的t Hooft反常匹配研究了该理论的整体性质.特胡夫特反常的计算包含了一个有趣的高群结构。我们还仔细考察了在大N和可靠的半经典条件下，这种运动学约束是如何在动力学中实现的，并且发现拓扑磁化率对π p 3-型对称性起着序参量的作用.在基本表象或伴随表象中引入费米子，我们发现手征对称性比通常情况下大，手征对称性破缺导致额外的p真空.没有动力学畴壁可以插入这些额外的真空，因为这样的对象必须在3-形式对称下充电，以匹配特胡夫特异常。
We consider the SU (N) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p. We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both 2π-periodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only ℤ N 1-form symmetry but also ℤ p 3-form symmetry, and we study the global nature of this theory from the recent’t Hooft anomaly matching. The computation of’t Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large-N and also the reliable semiclassics on ℝ 3× S 1, and we find that the topological susceptibility plays a role of the order parameter for the ℤ p 3-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by ℤ p, and it leads to the extra p vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the 3-form symmetry in order to match the’t Hooft anomaly.