Gauge-Dressed Complex Geometry and T-duality in Heterotic String Theories

TL;DR

This paper explores T-duality in heterotic string theories using gauge-dressed complex geometry, introducing a shifted metric and generalized structures to derive new duality rules.

Contribution

It introduces gauge-dressed complex geometry with a shifted metric and constructs an extended Born geometry satisfying hypercomplex algebra.

Findings

Derived a heterotic Buscher-like T-duality rule for gauge-dressed structures.

Constructed an extended Born geometry satisfying hypercomplex algebra.

Showed gauge-dressed structures facilitate T-duality analysis in heterotic strings.

Abstract

We study T-duality of $(p,q)$-hermitian geometries in backgrounds with non-Abelian gauge fields $A$ in heterotic string theories. We introduce a gauge-dressed complex geometry characterized by a shifted metric $\bar{g} = g + \frac{1}{2} \mathrm{Tr}(A^2)$, the closed 2-form $\omega$ and a quasi complex structure satisfying $\bar{J}^2 < 0$, but not necessarily $\bar{J}^2 = -1$. Utilizing the positive and negative chirality half generalized complex-like structures constructed by $(\bar{g}, \bar{J})$, we derive a heterotic Buscher-like rule for geometric quantities. We also demonstrate that the gauge-dressed structures can be used to construct an extended Born geometry that satisfies algebras of hypercomplex numbers.