Dimensional Duality

TL;DR

This paper introduces a new string duality called Dimensional Duality, showing that string theory on negatively curved manifolds effectively gains extra dimensions, with implications for D-branes and AdS/CFT systems.

Contribution

It presents a novel duality linking string theory on negatively curved spaces to higher-dimensional structures, expanding understanding of supercritical backgrounds.

Findings

String theory on negatively curved manifolds grows at least b_1 effective dimensions.

Winding currents produce a D-dual description involving Jacobian tori.

An AdS/CFT system provides a non-perturbative formulation of these backgrounds.

Abstract

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. Finally, we discuss generalizations of this new string duality.