Quantum Corrections to the Universal Hypermultiplet and Superspace

TL;DR

The paper addresses quantum corrections to the universal hypermultiplet moduli space in type II string compactifications with N=2 supergravity. It employs projective superspace and the hyperkähler cone framework to recast the problem in terms of hypermultiplet sigma-models with commuting isometries, enabling a tractable derivation of the one-loop correction. The main result is a superspace formulation in terms of a single homogeneous function G(\eta_1,\eta_2) that reproduces the known one-loop deformation and the corresponding metric, and a proposed nonperturbative metric induced by five-brane instantons described by F_UH with an \eta^{(4)} multiplet, highlighting symmetry-breaking patterns and potential extensions. The work thus connects HKC/QK geometry, Calderbank-Pedersen formalism, and projective superspace to provide a coherent description of perturbative and nonperturbative corrections to the universal hypermultiplet moduli space, with implications for cosmology and string phenomenology.

Abstract

We investigate quantum corrections to the effective action of the universal hypermultiplet in the language of projective superspace. We rederive the recently found one-loop correction to the universal hypermultiplet moduli space geometry. The deformed metric is described as a superspace action in terms of a single function, homogeneous of first degree. Our framework leads us to a natural proposal for the nonperturbative moduli space metric induced by five-brane instantons.