Enhanced gauge symmetry and winding modes in Double Field Theory

TL;DR

This paper demonstrates how string winding modes and enhanced gauge symmetries near the self-dual radius can be incorporated into double field theory, providing a consistent framework that captures the low energy effective action with non-geometric features.

Contribution

It introduces a novel double field theory formulation that includes winding modes and enhanced gauge symmetries, extending the understanding of string compactifications.

Findings

Explicit example of winding mode incorporation in double field theory

Derivation of effective gauge theory with enhanced symmetry at the self-dual radius

Construction of a non-geometric frame dependent on both coordinate and dual coordinate

Abstract

We provide an explicit example of how the string winding modes can be incorporated in double field theory. Our guiding case is the closed bosonic string compactified on a circle of radius close to the self-dual point, where some modes with non-zero winding or discrete momentum number become massless and enhance the $U(1) \times U(1)$ symmetry to $SU(2) \times SU(2)$. We compute three-point string scattering amplitudes of massless and slightly massive states, and extract the corresponding effective low energy gauge field theory. The enhanced gauge symmetry at the self-dual point and the Higgs-like mechanism arising when changing the compactification radius are examined in detail. The extra massless fields associated to the enhancement are incorporated into a generalized frame with $\frac{O(d+3,d+3)}{O(d+3)\times O(d+3)}$ structure, where $d$ is the number of non-compact dimensions. We devise a consistent double field theory action that reproduces the low energy string effective action with enhanced gauge symmetry. The construction requires a truly non-geometric frame which explicitly depends on both the compact coordinate along the circle and its dual.