The delta(0) Singularity in the Warped Mirabelli-Peskin Model

TL;DR

This paper demonstrates that the singularities arising from delta functions in the warped Mirabelli-Peskin model are canceled by the infinite sum of Kaluza-Klein modes, extending previous flat-space results to a warped background.

Contribution

It proves the cancellation of delta(0) singularities in a warped 5D super-Yang-Mills model, generalizing earlier flat-space findings to AdS_5 backgrounds.

Findings

Singularities are canceled by KK mode sums in warped models.

Explicit KK expansion of bulk propagator is provided.

Cancellation occurs perturbatively to all orders and loops.

Abstract

The Mirabelli-Peskin model is a 5D super-Yang-Mills theory compactified on an orbifold $S^1/Z_2$ with the 4D Wess-Zumino model localized on the boundaries (or branes). As the 5D gauge multiplet couples to 4D chiral multiplets through delta functions, the model contains singular terms proportional to $\delta(0)$ after integrating out a 5D auxiliary field. This belongs to the same type of singularity as what was first noticed by Horava in the orbifold compactification of heterotic string theory. Mirabelli-Peskin showed that this singularity was field-theoretically harmless by demonstrating its neat cancellation by the singularity produced by the infinite sum of Kaluza-Klein (KK) excitation modes of bulk propagator. In this paper, the similar cancellation is proved to occur also in a warped version of Mirabelli-Peskin model with the background of ${AdS}_5$. The bulk propagator of scalar component of 5D vector supermultiplet in the warped extra dimension is explicitly KK expanded. Then, its second derivatives by the coordinates of $S^1/Z_2$ generate a term proportional to $\delta(0)$ at the boundaries. The cancellation is considered to take place perturbatively to all orders of coupling constants as well as to all loops.