On the extension of a TCFT to the boundary of the moduli space

Details On the extension of a TCFT to the boundary of the moduli space On the extension of a TCFT to the boundary of the moduli space

2010-02-13

arxiv.org/abs/1002.2670v1

Mathematics

Quantum Algebra

15 pages, 7 figures

Scientific paper

The purpose of this paper is to describe an analogue of a construction of Costello in the context of finite-dimensional differential graded Frobenius algebras which produces closed forms on the decorated moduli space of Riemann surfaces. We show that this construction extends to a certain natural compactification of the moduli space which is associated to the modular closure of the associative operad, due to the absence of ultra-violet divergences in the finite-dimensional case. We demonstrate that this construction is equivalent to the "dual construction" of Kontsevich.

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