Coupling Constant Dependence of the Kaluza--Klein Spectrum in Five-Dimensional SQCD on S^1

TL;DR

This paper derives the exact Kaluza-Klein spectrum for a five-dimensional supersymmetric gauge theory on a circle, revealing how the spectrum depends on the coupling constant and connecting weak and strong coupling regimes.

Contribution

It provides an exact mass formula for KK modes in 5D SQCD on S^1 using Seiberg--Witten theory, elucidating the coupling dependence of the spectrum.

Findings

The lightest gauge KK state is stable across all moduli.

The lightest matter KK state decays more easily in certain moduli regions.

The spectrum smoothly transitions from weak to strong coupling regimes.

Abstract

We investigate the Kaluza--Klein (KK) spectrum of N=1 supersymmetric gauge theory compactified on a circle. We concentrate on a model with gauge group SU(2) and four massless matter fields in the fundamental representation. We derive the exact mass formula of KK modes by using Seiberg--Witten theory. From the mass formula and the D3-brane probe realization, we determine the spectrum of KK modes of matter fields and gauge fields. As a result, we find that the lightest KK state of gauge fields is stable for all the vacuum moduli space, while the lightest KK state of matter fields decays easier than other KK states in a region of the moduli space. The region becomes small as we decrease the five-dimensional gauge coupling constant g_5, and vanishes as we take the limit g_5->0. This result continuously connects the known KK spectrum in the weak coupling limit and that in the strong coupling limit.