T-duality can fail

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. (author)