SymTFTs for Continuous non-Abelian Symmetries

SymTFTs for Continuous non-Abelian Symmetries

19 Feb 2024 | Federico Bonetti, Michele Del Zotto, and Ruben Minasian
This paper introduces a new approach to describe continuous non-Abelian symmetries in quantum field theories (QFTs) using a topological field theory called SymTFT. The SymTFT is a (d+1)-dimensional topological field theory that captures the symmetry of a d-dimensional QFT. The main challenge is to describe continuous non-Abelian symmetries, which are more complex than discrete symmetries. The authors propose that the SymTFT for continuous non-Abelian symmetries is a free non-Abelian Yang-Mills theory at zero gauge coupling. This approach is supported by geometric engineering and holography. The authors show that the SymTFT for continuous non-Abelian symmetries can be derived from the duality between free Yang-Mills theory and the non-Abelian BF theory. They also provide evidence from geometric engineering and holography that this approach is valid. The results are applied to various examples, including SCFTs realized via geometric engineering and holographic SCFTs. The authors conclude that the SymTFT for continuous non-Abelian symmetries is a (d+1)-dimensional Yang-Mills theory at zero coupling, which is dual to the non-Abelian BF theory with the same gauge group. This result confirms the proposal in [30, 31] and provides a new perspective on the representation theory of non-Abelian symmetries. The paper also discusses the implications of this result for the study of topological defects and the interplay between symmetries and anomalies.This paper introduces a new approach to describe continuous non-Abelian symmetries in quantum field theories (QFTs) using a topological field theory called SymTFT. The SymTFT is a (d+1)-dimensional topological field theory that captures the symmetry of a d-dimensional QFT. The main challenge is to describe continuous non-Abelian symmetries, which are more complex than discrete symmetries. The authors propose that the SymTFT for continuous non-Abelian symmetries is a free non-Abelian Yang-Mills theory at zero gauge coupling. This approach is supported by geometric engineering and holography. The authors show that the SymTFT for continuous non-Abelian symmetries can be derived from the duality between free Yang-Mills theory and the non-Abelian BF theory. They also provide evidence from geometric engineering and holography that this approach is valid. The results are applied to various examples, including SCFTs realized via geometric engineering and holographic SCFTs. The authors conclude that the SymTFT for continuous non-Abelian symmetries is a (d+1)-dimensional Yang-Mills theory at zero coupling, which is dual to the non-Abelian BF theory with the same gauge group. This result confirms the proposal in [30, 31] and provides a new perspective on the representation theory of non-Abelian symmetries. The paper also discusses the implications of this result for the study of topological defects and the interplay between symmetries and anomalies.
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