19 Feb 2024 | Federico Bonetti, Michele Del Zotto, Ruben Minasian
This paper explores the SymTFT (Symmetry Topological Field Theory) for continuous non-Abelian symmetries, a generalization of the SymTFT that captures topological defects and operators in quantum field theories. The authors propose that the SymTFT for a QFT with a continuous non-Abelian symmetry is a $(d+1)$-dimensional free Yang-Mills theory at zero gauge coupling. This proposal is motivated by geometric engineering and holography, and it reconciles the SymTFT with the non-Abelian BF theory. The main results are derived using geometric engineering and holography, showing that the SymTFT for continuous non-Abelian symmetries can be described as a gauge theory in $d+1$ dimensions with gauge group $G$ at $g_{\mathrm{YM}}=0$. The flat subsector of this theory is dual to the non-Abelian BF theory with the same gauge group. The paper also discusses the representation theory of non-Abelian Lie groups and the interplay with ordinary global symmetries, such as anomalies and spontaneous breaking. The findings suggest a pathway to describe topological defects for space-time symmetries in terms of a gravitational $(d+1)$-dimensional bulk theory at zero coupling.This paper explores the SymTFT (Symmetry Topological Field Theory) for continuous non-Abelian symmetries, a generalization of the SymTFT that captures topological defects and operators in quantum field theories. The authors propose that the SymTFT for a QFT with a continuous non-Abelian symmetry is a $(d+1)$-dimensional free Yang-Mills theory at zero gauge coupling. This proposal is motivated by geometric engineering and holography, and it reconciles the SymTFT with the non-Abelian BF theory. The main results are derived using geometric engineering and holography, showing that the SymTFT for continuous non-Abelian symmetries can be described as a gauge theory in $d+1$ dimensions with gauge group $G$ at $g_{\mathrm{YM}}=0$. The flat subsector of this theory is dual to the non-Abelian BF theory with the same gauge group. The paper also discusses the representation theory of non-Abelian Lie groups and the interplay with ordinary global symmetries, such as anomalies and spontaneous breaking. The findings suggest a pathway to describe topological defects for space-time symmetries in terms of a gravitational $(d+1)$-dimensional bulk theory at zero coupling.