Let Y, Z be a pair of smooth coisotropic subvarieties in a smooth algebraic Poisson variety X. We show that any data of first order deformation of the structure sheaf OX to a sheaf of noncommutative algebras and of the sheaves OY and OZ to sheaves of right and left modules over the deformed algebra, respectively, gives rise to a Batalin-Vilkoviski algebra structure on the Tor-sheaf TorX q (OY ,...

Let Y, Z be a pair of smooth coisotropic subvarieties in a smooth algebraic Poisson variety X. We show that any data of first order deformation of the structure sheaf OX to a sheaf of noncommutative algebras and of the sheaves OY and OZ to sheaves of right and left modules over the deformed algebra, respectively, gives rise to a Batalin-Vilkoviski algebra structure on the Tor-sheaf TorX q (OY ,...

The Batalin-Vilkovisky method (BV ) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangi...

One may introduce at least three different Lie algebras in any Lagrangian field theory : (i) the Lie algebra of local BRST cohomology classes equipped with the odd Batalin-Vilkovisky antibracket, which has attracted considerable interest recently ; (ii) the Lie algebra of local conserved currents equipped with the Dickey bracket ; and (iii) the Lie algebra of conserved, integrated charges equip...

— In this paper, we show that the Givental group action on genus zero cohomological field theories, also known as formal Frobenius manifolds or hypercommutative algebras, naturally arises in the deformation theory of Batalin–Vilkovisky algebras. We prove that the Givental action is equal to an action of the trivialisations of the trivial circle action. This result relies on the equality of two ...

The most convenient tool to study the renormalization of a Lagrangian field theory invariant under non linear local or global symmetries is the proper solution to the master equation of the extended antifield formalism. It is shown that, from the knowledge of the BRST cohomology, it is possible to explicitly construct a further extension of the formalism containing all the observables of the th...

Canonical treatment of two dimensional gravity as an anomalous gauge theory ABSTRACT The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the BRST symmetry and the origin of SL(2, R) current algebra. From the same ...