Tailoring T-Duality Beyond the First Loop

Abstract

In this article we review a recent calculation of the two-loop $\sigma$-model corrections to the T-duality map in string theory. Using the effective action approach, and focusing on backgrounds with a single Abelian isometry, we give the $O(\alpha')$ modifications of the lowest-order duality transformations. The torsion plays an important role in the theory to $O(\alpha')$, because of the Chern-Simons couplings to the gauge fields that arise via dimensional reduction.Comment: 9 pages, Latex, no figures. Based on the talks given by N. Kaloper at the conferences Black Holes: Theory and Mathematical Aspects at Banff, AB, Canada and the $7^{th}~C^2GR^2A$ in Calgary, AB, Canada, May 31 - June 7, 199