The fate of discrete 1-form symmetries in 6d

Recently introduced generalized global symmetries have been useful in order to understand non-perturbative aspects of quantum field theories in four and lower dimensions. In this talk I will focus on 1-form symmetries of weakly coupled 6d supersymmetric gauge theories coupled to tensor multiplets and their interplay with large gauge transformations for dynamical tensor fields. In a non-trivial background for the global 1-form symmetry, this leads to an ambiguity of the effective field theory partition function. This anomaly is eliminated by the inclusion of BPS strings. However, the non-trivial 1-form background can induce fractional string charges which are not compatible with Dirac quantization, and hence the symmetry is absent. I will describe how the anomalous term serves as a tool to detect whether the discrete 1-form symmetries are realized in explicit examples originating from string compactifications. I will show how this is corroborated by finding that a non-trivial ambiguity is related to states, which are excitations of the 6d BPS strings and explicitly break the global 1-form symmetry. For 6d theories consistently coupled to gravity, this ambiguity of the partition function hints at the presence of a symmetry breaking tower of states. When the ambiguity is absent, the F-theory realization of the theories points to the gauging of the 1-form symmetries.

6th of October 2020, 14:30