Chiral anomaly in 5-dimensional orbifold field theory

Abstract

Chiral anomaly in quantum field theory is first calculated by Adler, Bell, and Jackiw in 1969. In this paper, 2-dimensional a 4-dimensional chiral anomalies are calculated in several approaches including Fujikawa``s path integral method and the direct calculation of the triangle diagram using the dimensional regularization.Then, we discuss the form of the chiral anomaly in 5 dimension. We give the orbifold structures $S^1/\mathbb{Z}_2$ and $S^1/\mathbb{Z}_2×\mathbb{Z}``_2$ to the 5-dimensional space and induce the anomaly term at the orbifold singularities. The 5-dimensional anomaly includes $F\tilde{F}$, the 4-dimensional ``chiral`` anomaly. We discuss in detail how this orbifold structures give the anomaly structures in 5-dimensional space.