New Dimensions for Wound Strings:The Modular Transform of Geometry to Topology Page: 1 of 29
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New Dimensions for Wound Strings:
THE MODULAR TRANSFORMATION OF GEOMETRY TO TOPOLOGY
John McGreevy', Eva Silverstein23, and David Starr2,3
1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
2SLAC and Department of Physics, Stanford University, Stanford, CA 94305-4060
3Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030
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 . 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.
Submitted to Physical Review D
Work supported in part by the US Department of Energy contract DE-AC02-76SF00515
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McGreevy, John; Silverstein, Eva & Starr, David. New Dimensions for Wound Strings:The Modular Transform of Geometry to Topology, article, December 18, 2006; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc877426/m1/1/: accessed February 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.