Related papers: Wheeled pro(p)file of Batalin-Vilkovisky formalism
Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras.
We develop a Lagrangian quantization formalism for a class of theories obtained by the restriction of the configuration space of gauge fields from a wider (parental) gauge theory. This formalism is based on application of the…
We derive equivariant localization formulas of Atiyah--Bott and cohomological field theory types in the Batalin-Vilkovisky formalism and discuss their applications in Poisson geometry and quantum field theory.
The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…
We give a definition of coisotropic morphisms of shifted Poisson (i.e. $P_n$) algebras which is a derived version of the classical notion of coisotropic submanifolds. Using this we prove that an intersection of coisotropic morphisms of…
We set up a Batalin-Vilkovisky Quantum Master Equation for open-closed string theory and show that the corresponding moduli spaces give rise to a solution, a generating function for their fundamental chains. The equation encodes the…
In previous work we introduced the notion of binomial cup-one algebras, which are differential graded algebras endowed with Steenrod $\cup_1$-products and compatible binomial operations. In this paper we show that binomial cup-one algebras…
The Lie-Rinehart algebra of a manifold M, defined by the Lie structure of the vector fields, their action and their module structure on the infinitely differentiable functions on M, is a common, diffeomorphism invariant, algebra for both…
We develop the technique of compactified correspondences and homotopies over one-dimensional base schemes, and illuminate the perfectness and the inverting of characteristic assumptions from the celebrating Voevodsky's strict homotopy…
In this paper, we construct groupoid coloured operads governing props and wheeled props, and show they are Koszul. This is accomplished by new biased definitions for (wheeled) props, and an extension of the theory of Groebner bases for…
Voevodsky outlined a conjectural programme that his slice filtration in motivic homotopy theory should give rise to a good theory of $\mathbb{A}^1$-invariant motivic cohomology. This paper achieves his vision in the generality of arbitrary…
We describe some recent development on the theory of formal Frobenius manifolds via a construction from differential Gerstenhaber-Batalin-Vilkovisk (DGBV) algebras and formulate a version of mirror symmetry conjecture: the extended…
Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional''…
We apply the modern Batalin-Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in the finite-dimensional case of fuzzy spaces. We further develop a generalization of this framework to theories that…
In recent work, Benjamin Schumacher and Michael D. Westmoreland investigate a version of quantum mechanics which they call modal quantum theory. This theory is obtained by instantiating the mathematical framework of Hilbert spaces with a…
The author, and independently De Concini, conjectured that the monodromy of the Casimir connection of a simple Lie algebra g is described by the quantum Weyl group operators of the quantum group U_h(g). The aim of this paper, and of its…
It is well known that a $Q$-manifold gives rise to an $L_\infty$-algebra structure on the tangent space at a fixed point of the homological vector field. From the field theory perspective this implies that the expansion of a classical…
This is the first of a series of two papers devoted to the partition function realization of Wilson surfaces in strict higher gauge theory. A higher version of the Kirillov-Kostant-Souriau theory of coadjoint orbits is presented based on…
The recently proposed generalized field method for solving the master equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic Lie algebras in 2-dimensions. The charge corresponding to BRST symmetry derived from this…
We begin the systematic study of cohomological Hecke operators of modifications of coherent sheaves on a smooth surface $X$, along a fixed proper curve $Z \subset X$. We develop the necessary geometric foundations in order to define the…