Connecting T-duality invariant theories

TL;DR

This paper demonstrates that the one-loop beta-functional vanishing condition in doubled formalism aligns with the equations of motion in generalized metric double field theory, highlighting a unified geometric framework.

Contribution

It establishes a correspondence between doubled formalism and double field theory through the common vanishing of a generalized Ricci tensor, suggesting a new doubled differential geometry.

Findings

The beta-functional vanishes iff the generalized Ricci tensor vanishes.

Both formalisms are governed by a common doubled differential geometry.

The work indicates a unified geometric understanding of string theory on torus fibrations.

Abstract

We show that the vanishing of the one-loop beta-functional of the doubled formalism (which describes string theory on a torus fibration in which the fibres are doubled) is the same as the equation of motion of the recently proposed generalised metric formulation of double field theory restricted to this background: both are the vanishing of a generalised Ricci tensor. That this tensor arises in both backgrounds indicates the importance of a new doubled differential geometry for understanding both constructions.