Celebratio Mathematica — Schwarz

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Works connected to Oleg V. Zaboronski

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M. Alexandrov, A. Schwarz, O. Zaboronsky, and M. Kontsevich: “The geometry of the master equation and topological quantum field theory,” Int. J. Mod. Phys. A 12 : 7 (1997), pp. 1405–1429. MR 1432574 Zbl 1073.81655 ArXiv hep-th/9502010 article

In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a \( QP \)-manifold, i.e. a supermanifold equipped with an odd vector field \( Q \) obeying \( \{Q,Q\} = 0 \) and with \( Q \)-invariant odd symplectic structure. We study geometry of \( QP \)-manifolds. In particular, we describe some construction of \( QP \)-manifolds and prove a classification theorem (under certain conditions).

We apply these geometric constructions to obtain in a natural way the action functionals of two-dimensional topological sigma-models and to show that the Chern–Simons theory in BV-formalism arises as a sigma-model with target space \( \Pi\mathcal{G} \). (Here \( \mathcal{G} \) stands for a Lie algebra and \( \Pi \) denotes parity inversion.)

Oleg V. Zaboronski	Related
Mikhail Dmitrievich Alexandrov	Related
Maksim Lvovich Kontsevich	Related

A. Schwarz and O. Zaboronsky: “Supersymmetry and localization,” Commun. Math. Phys. 183 : 2 (1997), pp. 463–476. MR 1461967 Zbl 0873.58003 ArXiv hep-th/9511112 article