The Dilaton Potential from N= 1*

TL;DR

This paper explores the superpotential derived from N=1* supersymmetric theory to understand the scalar potential for the string dilaton, revealing runaway behavior and stable vacua, with implications for gauge coupling values.

Contribution

It demonstrates how the superpotential from N=1* theory can generate a nontrivial dilaton potential with multiple vacua and potential stabilization at weak coupling.

Findings

Runaway behavior of the potential at generic parameters.

Existence of supersymmetric minima stabilizing the dilaton.

Proliferation of vacua in confining phases with increasing N.

Abstract

Recent understanding of {\cal N}=1* supersymmetric theory (mass deformed {\cal N}=4) has made it possible to find an exact superpotential which encodes the properties of the different phases of the theory. We consider this superpotential as an illustrative example for the source of a nontrivial scalar potential for the string theory dilaton and study its properties. The superpotential is characterized by the rank of the corresponding gauge group (N) and integers p,q,k labelling the different massive phases of the theory. For generic values of these parameters, we find the expected runaway behaviour of the potential to vanishing string coupling. But there are also supersymmetric minima at weak coupling stabilizing the dilaton field. An interesting property of this potential is that there is a proliferation of supersymmetric vacua in the confining phases, with the number of vacua increasing with N and leading to a kind of staircase potential. For a range of parameters, it is possible to obtain realistic values for the gauge coupling.