Anomalous terms in gauge theory : relevance of the structure group
Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking...
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus with a complex line , with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to . The converse statement is also true, namely a holomorphic bundle on which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton....