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Determinants of Laplacians in real line bundles over hyperbolic manifolds connected with quantum geometry of membranes

Authors
  • Goncharov, Yu.P.
Publication Date
Jan 01, 1990
Identifiers
DOI: 10.1007/BF00402263
OAI: oai:inspirehep.net:302270
Source
INSPIRE-HEP
Keywords
License
Unknown
External links

Abstract

The possibility is discussed of generalizing the Polyakov approach to strings on membranes and the connection of such a generalization with Thurston's classification of three-dimensional geometries. The important ingredients for computing a membrane path integral are the determinants of scalar Laplacians acting in real line bundles over three-dimensional closed manifolds. In the closed bosonic membrane case, such determinants are evaluated for a class of closed 3-manifolds of the H3/Г form with a discrete subgroup of isometries Г of the three-dimensional Lobachevsky space H3 and they are expressed in terms of the Selberg zeta function. Some further possible implications of the results obtained are also discussed.

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