Topological Field Theory Interpretation of String Topology |
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Authors: | Email author" target="_blank">Alberto S?CattaneoEmail author Jürg?Fr?hlich Bill?Pedrini |
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Institution: | (1) Institut für Theoretische Physik, ETH Hönggerberg, 8093 Zürich, Switzerland;(2) Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland |
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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, ) 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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