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

Abstract

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.

15 pages, 7 figures

References in corpus (6)

• Strebel differentials on stable curves and Kontsevich's proof of Witten's conjecture
• Feynman diagrams and minimal models for operadic algebras
• Abstract Hodge decomposition and minimal models for cyclic algebras
• Topological conformal field theories and gauge theories
• Noncommutative geometry and compactifications of the moduli space of curves
• Dual Feynman transform for modular operads