Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry

TL;DR

This paper investigates how closed bosonic strings behave in backgrounds with fluxes, revealing nonassociative geometry structures and their implications for conformal field theories through scattering amplitude analysis.

Contribution

It introduces a conformal field theory framework for flux backgrounds, derives a fluxed Virasoro-Shapiro amplitude, and uncovers nonassociative geometry via a deformed tri-product.

Findings

Derived fluxed Virasoro-Shapiro amplitude for tachyon scattering

Identified nonassociative target-space structure in R-flux backgrounds

Showed R-flux backgrounds flow to asymmetric conformal field theories

Abstract

We study closed bosonic strings propagating both in a flat background with constant H-flux and in its T-dual configurations. We define a conformal field theory capturing linear effects in the flux and compute scattering amplitudes of tachyons, where the Rogers dilogarithm plays a prominent role. For the scattering of four tachyons, a fluxed version of the Virasoro-Shapiro amplitude is derived and its pole structure is analyzed. In the case of an R-flux background obtained after three T-dualities, we find indications for a nonassociative target-space structure which can be described in terms of a deformed tri-product. Remarkably, this product is compatible with crossing symmetry of conformal correlation functions. We finally argue that the R-flux background flows to an asymmetric CFT.