Higher form symmetries and orbifolds in quantum gravity

Global symmetries in quantum field theory usually act on operators that are supported on points in space-time. It has been recently understood that there exist symmetries that only act on operators supported on higher dimensional submanifolds of space-time, such as lines, surfaces, etc. These are called higher form symmetries and often appear together with the usual global symmetries in a non-trivial structure called n-group. Whenever a quantum field theory admits a global discrete symmetry, this can be gauged to obtain a new theory, which is usually called the orbifold. The orbifold procedure in quantum field theory has been recently generalized to the case of higher form global symmetries. In string theory, an orbifold can be defined as the gauging of a global symmetry in the two-dimensional theory describing the degrees of freedom on a string. However, there might be obstructions, called ’t Hooft anomalies, that prevent the gauging of a global symmetry and can be problematic in a quantum gravity theory. The goal of the thesis is to analyze these possible anomalies and to verify their cancellation by a non-trivial 2-group symmetry in some simple models arising in string theory.