The low-energy effective action for perturbative heterotic strings on $K_3 \times T^2$ and the d=4 N=2 vector-tensor multiplet

TL;DR

This paper constructs a new low-energy effective action for heterotic strings on K_3 imes T^2, revealing how the antisymmetric tensor and dilaton fit into N=2 supergravity multiplets using superconformal methods.

Contribution

It introduces a novel version of the heterotic effective action where the antisymmetric tensor replaces the axion, clarifying its multiplet structure in N=2 supergravity.

Findings

The antisymmetric tensor does not transform into the dilaton-dilatini system in the string frame.

The heterotic dilaton resides in a hypermultiplet, not a vector-tensor multiplet.

The antisymmetric tensor is part of the gravitational multiplet.

Abstract

We consider d=4 N=2 supergravity theories which serve as low-energy effective actions for heterotic strings on K_3 \times T^2. At the perturbative level we construct a new version of the heterotic effective action in which the axion has been traded for an antisymmetric tensor field. In the string frame the antisymmetric tensor doesn't transform under Poincar\'e supersymmetry into the dilaton-dilatini system. This indicates that in this frame the antisymmetric tensor field and the dilaton are not contained in an N=2 vector-tensor multiplet. Instead, we find that the heterotic dilaton is part of a compensating hypermultiplet, whereas the antisymmetric tensor is part of the gravitational multiplet. In order to obtain our results we use superconformal techniques. This enables us to comment on the range of applicability of this particular framework.