The strength of small-instanton amplitudes in gauge theories with compact extra dimensions

TL;DR

This paper investigates how instanton effects in 5D gauge theories with compact extra dimensions can dominate at small scales, showing exponential growth of amplitudes depending on matter content and using deconstruction for UV control.

Contribution

It provides a detailed instanton calculation in 5D theories on a circle and demonstrates the exponential growth of small-instanton amplitudes with controlled UV regularization.

Findings

Instantons of size rho << R can dominate amplitudes.

Small-instanton amplitudes grow exponentially as e^{O(1) R/rho}.

The matter content influences the dominance of small instantons.

Abstract

We study instanton effects in theories with compact extra dimensions. We perform an instanton calculation in a 5d theory on a circle of radius R, with gauge, scalar, and fermion fields in the bulk of the extra dimension. We show that, depending on the matter content, instantons of size rho << R can dominate the amplitude. Using deconstruction as an ultraviolet definition of the theory allows us to show, in a controlled approximation, that for a small number of bulk fermions, the amplitude for small size instantons exponentially grows as e^{O(1)R/rho}.