U-Duality of Born-Infeld on the Noncommutative Two-Torus

TL;DR

This paper demonstrates that Born-Infeld theory on a noncommutative two-torus exhibits manifest T-duality and U-duality symmetries, revealing deep invariances in the string theory compactification, despite some issues with parameter identification.

Contribution

It establishes the full T-duality and U-duality invariance of Born-Infeld theory on the noncommutative two-torus, including fluctuations, and discusses the challenges in relating noncommutative parameters to B-field moduli.

Findings

Theory is invariant under SO(2,2;Z) T-duality.

BPS mass exhibits SL(3,Z) x SL(2,Z) U-duality symmetry.

Identification of noncommutative parameter with B-field modulus is problematic at finite volume.

Abstract

We discuss Born-Infeld on the noncommutative two-torus as a description of compactified string theory. We show that the resulting theory, including the fluctuations, is manifestly invariant under the T-duality group SO(2,2;Z). The BPS mass even has a full SL(3,Z)xSL(2,Z) U-duality symmetry. The direct identification of the noncommutative parameter \theta with the B-field modulus however seems to be problematic at finite volume.