Dimensional duality

We show that string theory on a compact negatively curved manifold, preserving a $U(1{)}^{b_1}$ winding symmetry, grows at least $b_1$ new effective dimensions as the space shrinks. The winding currents yield a “D-dual” description of a Riemann surface of genus $h$ in terms of its $2h$ dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the world sheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a $b_1$-torus. In particular, we present an anti-de Sitter (AdS)/conformal field theory (CFT) system which offers a nonperturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.