The Effective K\"ahler Potential And Extra Space-Time Dimensions

TL;DR

This paper investigates how extra spatial dimensions influence the effective K"ahler potential in supersymmetric gauge theories, revealing that quantum corrections grow with the size of the extra dimension, indicating higher-dimensional effects.

Contribution

It provides a detailed analysis of the relationship between the K"ahler metric and gauge couplings in theories with extra dimensions, highlighting conditions for the absence of radiative corrections.

Findings

Quantum corrections increase with the radius of the extra dimension.

The relation between K"ahler metric and gauge couplings is explicitly derived.

Higher-dimensional effects manifest in the growth of quantum corrections.

Abstract

The effects of extra space-time dimensions on the Wilsonian effective K\"ahler potential and the perturbative one loop effective K\"ahler potential are determined within the framework of an Abelian gauge theory with N=2 supersymmetric field content. The relation between the K\"ahler metric and the effective gauge couplings which leads to the absence of radiative corrections to the K\"ahler potential is expressed as a function of the radius of compactification of a fifth dimension. In general, the quantum corrections to the low energy K\"ahler potential are shown to grow with this radius reflecting the underlying higher dimensional nature of the theory.