Effective Actions near Singularities

TL;DR

This paper derives a quantum-corrected, non-singular effective action for heterotic string compactified on K3 x T^2 near a gauge symmetry enhancement point, maintaining SU(2) and SL(2,Z) symmetries.

Contribution

It introduces a method to 'integrate in' light vector multiplets to obtain a consistent, SU(2) invariant effective action near singularities.

Findings

Derived a non-singular effective action near T=U

Maintained SU(2) and SL(2,Z) symmetries in the effective theory

Recovered known 5D SU(2) invariant action in decompactification limit

Abstract

We study the heterotic string compactified on K3 x T^2 near the line T=U, where the effective action becomes singular due to an SU(2) gauge symmetry enhancement. By `integrating in' the light W^\pm vector multiplets we derive a quantum corrected effective action which is manifestly SU(2) invariant and non-singular. This effective action is found to be consistent with a residual SL(2,Z) quantum symmetry on the line T=U. In an appropriate decompactification limit, we recover the known SU(2) invariant action in five dimensions.