Feynman diagrams and minimal models for operadic algebras

Chuang, J. & Lazarev, A. (2010). Feynman diagrams and minimal models for operadic algebras. Journal of the London Mathematical Society, 81(2), pp. 317-337. doi: 10.1112/jlms/jdp073

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Abstract

We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A∞-algebras. Furthermore, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced by sums over general Feynman graphs. As a by-product of our work we prove gauge-independence of Kontsevich's ‘dual construction’ producing graph cohomology classes from contractible differential graded Frobenius algebras.

Item Type: Article
Uncontrolled Keywords: STRING FIELD-THEORY, HOMOTOPY ALGEBRAS
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/187

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