Two and three loop alpha' corrections to T-duality: Kasner and Schwarzschild

TL;DR

This paper computes higher-loop alpha' corrections to T-duality for Kasner and Schwarzschild metrics in bosonic string theory, enabling the precise determination of T-duality rules at three loops and introducing a new class of massless geometries.

Contribution

It provides the first detailed calculation of two and three loop alpha' corrections to T-duality for specific string backgrounds, fixing the covariant form of T-duality rules at three loops.

Findings

Alpha' corrections are explicitly calculated for Kasner and Schwarzschild metrics.

The covariant form of T-duality rules is uniquely fixed at three loops.

A new class of massless geometries as T-duals of Schwarzschild is presented.

Abstract

Two and three loop alpha' corrections are calculated for Kasner and Schwarzschild metrics, and their T-duals, in the bosonic string theory. These metrics are used to obtain the two and three loop alpha' corrections to T-duality. It is noted in particular that the inclusion of alpha' corrections and the requirement of consistency with the alpha'-corrected T-duality for the Kasner and Schwarzschild metrics enables one to fix uniquely the covariant form of the T-duality rules at three loops. As a generalization of the T-dual of the Schwarzschild geometry a class of massless geometries is presented.