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

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))similar to Tr (f((2)) boolean AND f((2))). We show that suitable mixed anomalies involving the gauge field f((2)) and ordinary 0-form global symmetries, such as flavor or Poincare 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.

Automated summary

The study of six-dimensional quantum field theories reveals the presence of mixed anomalies in little string theories but their absence in SCFTs. This discovery provides an algorithm for computing the 't Hooft anomalies of most SCFTs. Furthermore, it is proven that the a-type Weyl anomaly of all SCFTs with a tensor branch must be positive.