Duality Beyond the First Loop

Abstract

In this article we give a calculation of the two-loop $\sigma$-model corrections to the T-duality map in string theory. We use the effective action approach, and analyze two-loop corrections in a specific subtraction scheme. Focusing on backgrounds which have a single Abelian isometry, we find the explicit form for the $O({\alpha }^{\prime })$ modifications of the lowest order duality transformations. Rather surprisingly, the manifest two-loop duality depends crucially on the torsion field. In contrast to the dilaton and metric fields, which are merely passive spectators, the torsion plays a more active role, because of the anomalous couplings to the gauge fields that arise via dimensional reduction. Our results support the interpretation of T-duality as an expansion in the inverse string tension ${\alpha }^{\prime }$, and its order-by-order realization as a manifest symmetry of the full string theory.

26 pages, latex, no figures. Several typos corrected, and references to Nucl. Phys. B405 (1993) 109 by E. Kiritsis and Nucl. Phys. B411 (1994) 487 by A. Giveon and E. Kiritsis added

References in corpus (1)

• Duality and Dilaton

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