Instanton-induced scalar potential for the universal hypermultiplet

TL;DR

This paper derives the scalar potential in N=2 supergravity with a hypermultiplet, using solutions to the Toda equation influenced by Eisenstein series, revealing instanton effects on the moduli space.

Contribution

It provides an explicit instanton-corrected scalar potential for the universal hypermultiplet using integrable Toda equations and Eisenstein series, advancing understanding of moduli space dynamics.

Findings

Explicit scalar potential solution involving Eisenstein series E_{3/2}

Connection between Toda equation solutions and hypermultiplet moduli space

Gauging of isometries affects the scalar potential structure

Abstract

We calculate the scalar potential in the gauged N=2 supergravity with a single hypermultiplet, whose generic quaternionic moduli space metric has an abelian isometry. This isometry is gauged by the use of a graviphoton gauge field. The hypermultiplet metric and the scalar potential are both governed by the single real potential that is a solution to the 3d (integrable) continuous Toda equation. An explicit solution, controlled by the Eisenstein series E_{3/2}, is found in the case of the D-instanton-corrected universal hypermultilet moduli space metric having an U(1)xU(1) isometry, with one of the isometries being gauged.