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Correlation functions for massive fermions with background instantons

by Wen-Yuan Ai, Juan S. Cruz, Björn Garbrecht, Carlos Tamarit

Submission summary

Authors (as registered SciPost users):

Wen-Yuan Ai · Björn Garbrecht

Abstract

We derive correlation functions for fermions with a complex mass in BPST instanton backgrounds in the presence of a general vacuum angle. For this purpose, we first build the Green's functions in the one-instanton background in Euclidean space through a spectral sum in terms of the eigenmodes for the massless case. While this is straightforward for a real mass term, an additional basis transformation among the massless modes of opposite eigenvalues is necessary for a complex mass term. We also construct the Green's functions in real time and relate this approach to recent developments on the theory of vacuum transitions in Minkowski spacetime. These results are then used in order to compute the correlation functions for massive fermions by summing over the background instantons. In these correlation functions, if the infinite-volume limit is taken before the sum over topological sectors, the chiral phases from the mass terms and from the instanton effects are aligned, such that, in absence of additional phases, these do not give rise to observable effects that would violate charge-parity symmetry.