Global anomaly

In theoretical physics, a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformation that would otherwise be preserved in the classical theory. This leads to an inconsistency in the theory because the space of configurations which is being integrated over in the functional integral involves both a configuration and the same configuration after a large gauge transformation has acted upon it and the sum of all such contributions is zero and the space of configurations cannot be split into connected components for which the integral is nonzero.

Alternatively, the existence of a global anomaly implies that the measure of Feynman's functional integral cannot be defined globally.

The adjective "global" refers to the properties of a group that are not visible locally. For example, all features of a discrete group (as opposed to a Lie group) are global in character.

A famous example is an SU(2) Yang–Mills theory in 4D with an odd number of chiral fermions transforming as doublets under SU(2).

Many types of global anomalies must cancel for a theory to be consistent. An example is modular invariance, the requirement of anomaly cancellation for a part of a gravitational anomaly that deals with the large diffeomorphisms over two dimensional worldsheets of genus 1 or more.