2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories

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 $J^{(2)}\sim \ast \text{Tr}\left(f^{(2)}\wedge f^{(2)}\right)$. 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, $a>0$.

56 pages; minor edits and added references

References in corpus (8)

• Generalized Global Symmetries
• Anomaly polynomial of general 6d SCFTs
• Higher-form symmetries of 6d and 5d theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• Discrete Theta Angles, Symmetries and Anomalies
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• Tutorial on Scale and Conformal Symmetries in Diverse Dimensions
• Chiral anomalies in higher-derivative supersymmetric 6D gauge theories

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