The Intriguing Structure of Non-geometric Frames in String Theory

TL;DR

This paper explores the structure of non-geometric frames in string theory, showing how they relate to geometric frames via $eta$-transforms, and introduces a Lie algebroid framework to describe effective actions in these frames.

Contribution

It introduces a Lie algebroid formalism for non-geometric string backgrounds and demonstrates its consistency with the low-energy effective action of superstrings.

Findings

Existence of natural field redefinitions for non-geometric frames.

Representation of the effective action using Lie algebroid geometry.

Connection of the formalism to double field theory and T-folds.

Abstract

Non-geometric frames in string theory are related to the geometric ones by certain local O(D,D) transformations, the so-called $\beta$-transforms. For each such transformation, we show that there exists both a natural field redefinition of the metric and the Kalb-Ramond two-form as well as an associated Lie algebroid. We furthermore prove that the all-order low-energy effective action of the superstring, written in terms of the redefined fields, can be expressed through differential-geometric objects of the corresponding Lie algebroid. Thus, the latter provides a natural framework for effective superstring actions in non-geometric frames. Relations of this new formalism to double field theory and to the description of non-geometric backgrounds such as T-folds are discussed as well.