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Topological field theory interpretation of string topology


Cattaneo, A S; Fröhlich, J; Pedrini, B (2003). Topological field theory interpretation of string topology. Communications in Mathematical Physics, 240(3):397-421.

Abstract

The string bracket introduced by Chas and Sullivan is reinterpreted from the point of view of topological field theories in the Batalin–Vilkovisky or BRST formalisms. Namely, topological action functionals for gauge fields (generalizing Chern–Simons and BF theories) are considered together with generalized Wilson loops. The latter generate a (Poisson or Gerstenhaber) algebra of functionals with values in the S1-equivariant cohomology of the loop space of the manifold on which the theory is defined. It is proved that, in the case of GL(n,C) with standard representation, the (Poisson or BV) bracket of two generalized Wilson loops applied to two cycles is the same as the generalized Wilson loop applied to the string bracket of the cycles. Generalizations to other groups are briefly described.

The string bracket introduced by Chas and Sullivan is reinterpreted from the point of view of topological field theories in the Batalin–Vilkovisky or BRST formalisms. Namely, topological action functionals for gauge fields (generalizing Chern–Simons and BF theories) are considered together with generalized Wilson loops. The latter generate a (Poisson or Gerstenhaber) algebra of functionals with values in the S1-equivariant cohomology of the loop space of the manifold on which the theory is defined. It is proved that, in the case of GL(n,C) with standard representation, the (Poisson or BV) bracket of two generalized Wilson loops applied to two cycles is the same as the generalized Wilson loop applied to the string bracket of the cycles. Generalizations to other groups are briefly described.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2003
Deposited On:27 Jan 2010 12:30
Last Modified:05 Apr 2016 13:25
Publisher:Springer
ISSN:0010-3616
Publisher DOI:10.1007/s00220-003-0917-2
Permanent URL: http://doi.org/10.5167/uzh-21860

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