Dimensional Duality

Understand

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 worldsheet 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 AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds.