Symmetry enhancement interpolation, non-commutativity and Double Field Theory

TL;DR

This paper develops a moduli-dependent effective field theory for heterotic string compactifications, incorporating non-commutative geometry and Double Field Theory to reproduce gauge symmetry enhancements and string amplitude features.

Contribution

It introduces a novel effective field theory framework that includes non-commutative products and double periodic coordinates to model gauge symmetry enhancements in string compactifications.

Findings

Reproduces gauge symmetry enhancement-breaking effects across moduli space.

Incorporates non-commutative geometry to match string amplitude results.

Extends low energy effective theories with new vector and scalar fields.

Abstract

We present a moduli dependent target space effective field theory action for (truncated) heterotic string toroidal compactifications. When moving continuously along moduli space, the stringy gauge symmetry enhancement-breaking effects, which occur at particular points of moduli space, are reproduced. Besides the expected fields, originated in the ten dimensional low energy effective theory, a new vector and scalar fields are included. These fields depend on "double periodic coordinates" as usually introduced in Double Field Theory. Their mode expansion encodes information about string states, carrying winding and KK momenta, associated to gauge symmetry enhancements. Interestingly enough, it is found that a non-commutative product, which introduces an intrinsic non-commutativity on the compact target space, is required in order to make contact with string theory amplitude results.