Quantum Field Theory as Effective BV Theory from Chern-Simons

Abstract

The general procedure for obtaining explicit expressions for all cohomologies of N.Berkovits's operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern-Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of "singular" point from the perspective of the suggested method for cohomology evaluation. For arbitrary "regular" point the same technique results in AKSZ(Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern-Simons theory (BF theory) in accord with [2,3].

34 pages, 15 figures, references added. Body of paper authored by Dmitry Krotov, Andrei Losev, appendix written with A.Gorodentsev

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• Taming open/closed string duality with a Losev trick
• From simplicial Chern-Simons theory to the shadow invariant I
• Materializing Superghosts
• The Derived Pure Spinor Formalism as an Equivalence of Categories
• Six-dimensional supermultiplets from bundles on projective spaces
• BV Quantization
• Topics in Open Topological Strings