Universality in Anomaly Flow

TL;DR

This paper demonstrates the universality of anomaly flow driven by an Aharonov-Bohm phase in both flat and warped extra-dimensional spacetimes, revealing how anomalies depend on geometric and boundary conditions.

Contribution

It shows that anomaly coefficients in gauge theories with orbifold boundary conditions depend on the AB phase, warp factor, and boundary conditions, but not on fermion bulk masses.

Findings

Anomaly coefficients are expressed via gauge field wave functions at branes.

Anomaly flow varies smoothly with the AB phase in RS space.

Anomaly coefficients depend on boundary conditions and warp factor, but not on fermion bulk masses.

Abstract

Universality in anomaly flow by an Aharonov-Bohm (AB) phase $\theta_H$ is shown in the flat $M^4 \times (S^1/Z_2)$ spacetime and in the Randall-Sundrum (RS) warped space. We analyze $SU(2)$ gauge theory with doublet fermions. With orbifold boundary conditions the $U(1)$ part of gauge symmetry remains unbroken at $\theta_H = 0$ and $\pi$. Chiral anomalies smoothly vary with $\theta_H$ in the RS space. It is shown that anomaly coefficients associated with this anomaly flow are expressed in terms of the values of the wave functions of gauge fields at the UV and IR branes in the RS space. The anomaly coefficients depend on $\theta_H$, the warp factor of the RS space, and the orbifold boundary conditions for fermions, but not on the bulk mass parameters of fermions.