Journal of High Energy Physics (Apr 2021)

2-Group global symmetries and anomalies in six-dimensional quantum field theories

  • Clay Córdova,
  • Thomas T. Dumitrescu,
  • Kenneth Intriligator

DOI
https://doi.org/10.1007/JHEP04(2021)252
Journal volume & issue
Vol. 2021, no. 4
pp. 1 – 46

Abstract

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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 f (2), naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J (2) ∼ ∗Tr (f (2) ∧ f (2)). We show that suitable mixed anomalies involving the gauge field f (2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J (2). 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 a-type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.

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