Abstract
We discuss a parity breaking in theories of fermions, which are trapped inside four-manifolds with boundaries. Even though these theories are parity-invariant at the classical level, the radiative corrections induce parityviolating boundary terms. The effect is present in both gauge and gravitational sectors.
Highlights
In this article we review the recent results [1, 2] concerning parity anomalies in quantum field theories (QFT) on four-dimensional manifolds with boundaries
Where “..." stands for parity-even contributions. Later on these results were generalised to a gravitational sector [18,19,20]
A parity anomaly can be defined in arbitrary dimension via Eq (5), strictly speaking, this expression does not make any sense, unless one introduces the regularisation
Summary
In this article we review the recent results [1, 2] concerning parity anomalies in quantum field theories (QFT) on four-dimensional manifolds with boundaries. Parity anomalies were discovered in the context of massless gauge theories on odddimensional manifolds without boundaries [3, 4]. In this paper we consider a 4-dimensional QFT, where Dirac fermions “live" inside the manifold M of a finite size and can not penetrate through the boundary ∂M. We will demonstrate that existence of a boundary creates a spectral asymmetry, which results in a presence of parity-violating boundary terms in the one-loop effective action.
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