2-group global symmetries and anomalies in six-dimensional quantum field theories
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Publication:2032628
DOI10.1007/JHEP04(2021)252zbMATH Open1462.81128arXiv2009.00138OpenAlexW3157332282MaRDI QIDQ2032628
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Publication date: 11 June 2021
Published in: (Search for Journal in Brave)
Abstract: We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength , naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current . We show that suitable mixed anomalies involving the gauge field and ordinary 0-form global symmetries, such as flavor or Poincar'e symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current . We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the 't Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the -type Weyl anomaly of all SCFTs with a tensor branch must be positive, .
Full work available at URL: https://arxiv.org/abs/2009.00138
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