2020/09/07 by Clay Cordova, Clay Córdova, Thomas T. Dumitrescu +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anomaly (physics) #Black Holes and Theoretical Physics #Gauge anomaly #Gauge symmetry #Gauge theory #Global symmetry #Instanton #Massless particle #Mixed anomaly #Quantum Chromodynamics and Particle Interactions #String (physics) #Symmetry (geometry) #hep-th
paper · pdf · doi:10.1007/jhep04(2021)252
56 pages; minor edits and added references
arxiv created 2020/09/07 · openalex created_date 2020/09/08 · openalex publication_date 2021/04/01 · arxiv updated 2021/05/12 · openalex updated_date 2026/08/06
A bstract 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.