Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-12-13
Phys.Rev.D75:044025,2007
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, harvmac big. v2: references and KITP preprint number added, minor changes
Scientific paper
10.1103/PhysRevD.75.044025
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.
McGreevy John
Silverstein Eva
Starr David
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