T-duality with $H$-flux for $2d$ $\sigma$-models

TL;DR

This paper develops a comprehensive framework for graded T-duality in two-dimensional sigma models with H-flux, extending T-duality to its most general form in Type II String Theory, and introduces the graded Hori morphism.

Contribution

It introduces the graded Hori morphism, establishing the most general form of T-duality for 2D sigma models with H-flux in Type II String Theory.

Findings

Established graded T-duality for 2D sigma models with H-flux.

Defined the graded Hori morphism compatible with graded fields.

Connected T-duality with the Jacobi property of graded fields.

Abstract

In this paper, we establish graded T-duality for $2d$ $\sigma$-models with $H$-flux after localization. This establishes the most general version of T-duality for Type II String Theory. The graded T-duality map, which we call {\bf graded Hori morphism}, is compatible with the Jacobi property of the graded fields, that was earlier studied in \cite{HM21}. Also included are some open problems/conjectures.