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arXiv · 2503.04546

Symmetry Topological Field Theory for Flavor Symmetry

Qiang Jia·Ran Luo·Jiahua Tian·Yi-Nan Wang·Yi Zhang
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Abstract

In this Letter, we demonstrate that the Symmetry Topological Field Theory (SymTFT) associated to a Quantum Field Theory (QFT) with continuous non-abelian $G$-flavor symmetry is a $BF$-theory with gauge group $G$. We show that gauging $G$-symmetry with a flat connection yields a theory with global symmetry characterized by exchanging the conjugate variables in the quantization of $BF$-theory. We construct the extended operators that generate the $G$-flavor symmetry and the $(d-2)$-form $\text{Rep}(G)$-symmetry of the gauged QFT. We demonstrate that $BF$-theory arises as the theory characterizing $G$-flavor symmetry of a QFT in the AdS/CFT setup. 't Hooft anomalies of the $G$-flavor symmetry are realized as extra terms in the action.

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Qiang Jia, Ran Luo, Jiahua Tian, Yi-Nan Wang, Yi Zhang. 2025-03-06. Symmetry Topological Field Theory for Flavor Symmetry. https://arxiv.org/abs/2503.04546

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