R-Symmetry and the Topological Twist of N=2 Effective Supergravities of Heterotic Strings

TL;DR

This paper explores R-symmetries in N=2 supergravity theories derived from heterotic strings, demonstrating how they enable topological twisting and lead to coupled instanton equations involving gravitational and gauge fields.

Contribution

It identifies the existence of a suitable R-symmetry in heterotic N=2 supergravities that allows topological twisting and formulates the resulting coupled instanton equations.

Findings

Existence of continuous R-symmetry in classical models.

Emergence of a discrete R-group in quantum-corrected models.

Formulation of coupled instanton equations involving gravity and gauge fields.

Abstract

We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R-symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the tree-level classical special manifolds $ST(n)=SU(1,1)/U(1)\times SO(2,n)/(SO(2)$ $\times SO(n))$ R-symmetry with the specified properties is a continuous symmetry, but for the quantum corrected manifolds ${\hat {ST}}(n)$ a discrete R--group of electric--magnetic duality rotations is sufficient and we argue that it exists.