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The Geometry of the Master Equation and Topological Quantum Field Theory | | M. Alexandrov
; M. Kontsevich
; A. Schwarz
; O. Zaboronsky
; | | Date: |
7 Feb 1995 | | Journal: | Int.J.Mod.Phys. A12 (1997) 1405-1430 | | Abstract: | In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a superm 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 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 $Pi {cal G}$. (Here ${cal G}$ stands for a Lie algebra and $Pi$ denotes parity inversion.) | | Source: | arXiv, hep-th/9502010 | | Services: | Forum | Review | PDF | Favorites | |
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