Dual dilaton with $\mathcal{R}$ and $\mathcal{Q}$ fluxes

TL;DR

This paper extends the geometric framework of string theory effective actions by incorporating a dual dilaton alongside fluxes  and , completing the description of T-dual fluxes in a Courant algebroid setting.

Contribution

It introduces a dual dilaton into the geometric formulation of string effective actions with  and  fluxes, completing the T-duality symmetric description.

Findings

Reproduced the NS-NS sector of type II supergravity action.

Derived an action involving inverse metric and bivector with  and  fluxes.

Incorporated the dual dilaton into the geometric framework.

Abstract

In previous works we showed that a Courant algebroid in a particular frame and the differential geometry of the sum bundle $TM \oplus T^*M$ provide a very natural geometric setting for a sector of the low energy effective limit of type II superstring theories (Supergravity theory). Given our geometric and algebraic considerations, we reproduced the NS-NS sector of the closed bosonic effective type II sting action, and an action for the inverse metric $G^{-1}$ and the bivector $\Pi$, related to the tensors for closed strings as $(g+B)^{-1} = (G^{-1} +\Pi)$. The action depended on the stringy T-dual fluxes $\mathcal{R}$ and $\mathcal{Q}$, but the dual dilaton was missing. This short paper fills the gap.