New dimensions for wound strings: The modular transformation of geometry to topology
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
- SLAC and Department of Physics, Stanford University, Stanford, California 94305-4060 (United States)
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 E. Silverstein, Phys. Rev. D 73, 086004 (2006).. 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.
- OSTI ID:
- 21011090
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 75, Issue 4; Other Information: DOI: 10.1103/PhysRevD.75.044025; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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