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arXiv · hep-th/0612121

New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology

John McGreevy·Eva Silverstein·David Starr
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Abstract

We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative sectional curvature on a compact Riemannian manifold to exponential growth of its fundamental group, which translates in string theory to a higher effective central charge arising from winding strings. This exponential density of winding modes is related by modular invariance to the infrared small perturbation spectrum. Using self-consistent approximations valid at large radius, we analyze this correspondence explicitly in a broad set of time-dependent solutions, finding precise agreement between the effective central charge and the corresponding infrared small perturbation spectrum. This indicates a basic relation between geometry, topology, and dimensionality in string theory.

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John McGreevy, Eva Silverstein, David Starr. 2007-01-03. New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology. https://doi.org/10.1103/physrevd.75.044025

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