Quantum field theory as effective BV theory from Chern–Simons

2006/03/31 by Dmitry Krotov, A. Losev, Andrei Losev +1
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Chern–Simons theory #Cohomology #Effective action #Field (mathematics) #Field theory (psychology) #Gauge theory #K-theory (physics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum field theory #Quantum mechanics #Theoretical physics #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2008.07.021

published as Nucl.Phys.B806:529-566,2009 · 34 pages, 15 figures, references added. Body of paper authored by Dmitry Krotov, Andrei Losev, appendix written with A.Gorodentsev

openalex publication_date 2008/07/31 · arxiv created 2008/08/04 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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].

Citations

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