New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology
arXiv:hep-th/0612121 · doi:10.1103/PhysRevD.75.044025
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.
28 pages, harvmac big. v2: references and KITP preprint number added, minor changes
References in corpus (7)
- Cosmological solutions of supercritical string theory
- Worldsheet CFTs for Flat Monodrofolds
- Supercritical stability, transitions and (pseudo)tachyons
- Supercritical N = 2 string theory
- Groups of Intermediate Growth: an Introduction for Beginners
- Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus
- De Sitter Quantum Mechanics and Inflationary Matrix Cosmology of Self-tuned Universe
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