T-Duality Can Fail
Paul S. Aspinwall, M. Ronen Plesser
TL;DR
This paper questions the exactness of T-duality in string theory once nonperturbative effects are included, focusing on the heterotic string on K3$\times T^2$ with $N=2$ in four dimensions. By exploiting a dual Type IIA description and a holonomy-based perspective, it shows that nonperturbative corrections modify the torus moduli space, breaking the expected $R\leftrightarrow 1/R$ symmetry and suggesting that dualities require large amounts of supersymmetry to be meaningful. The analysis contrasts unbroken fibre-wise duality in a two-parameter K3 model with broken T-duality when a CY threefold replaces K3, highlighting that monodromy and discriminant structures prevent a global duality group from existing at finite coupling. A holonomy-based argument further indicates dualities arise only in rigid (highly symmetric) moduli spaces, implying that the classical modular invariance of the torus can be quantum-mechanically broken in less supersymmetric compactifications. Overall, the work emphasizes that dualities are contextual, tied to SUSY and holonomy, and that string theory may invalidate naïve, geometry-based notions of size and modular symmetry in realistic, nonperturbative settings.
Abstract
We show that T-duality can be broken by nonperturbative effects in string coupling. The T-duality in question is that of the 2-torus when the heterotic string is compactified on K3 x T2. This case is compared carefully to a situation where T-duality appears to work. A holonomy argument is presented to show that T-dualities (and general U-dualities) should only be expected for large amounts of supersymmetry. This breaking of R <-> 1/R symmetry raises some interesting questions in string theory which we discuss. Finally we discuss how the classical modular group of a 2-torus appears to be broken too.