Related papers: BV actions for extended geometry
The abstract notion of Tamarkin-Tsygan calculus with duality gives Batalin- Vilkovisky structures in a general setting. We apply this technique to the case of Van den Bergh duality for algebras to prove that Calabi-Yau algebras are…
Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L-infinity-quasi-isomorphic to its cohomology. The construction of the L-infinity map is given in terms of…
I show that a summation over ribbon graphs with legs gives the construction of the solutions to the noncommutative Batalin-Vilkovisky equation, including the equivariant version. This generalizes the known construction of A-infinity algebra…
In this paper we analyse a certain type of higher derivative gauge theories which are known to possess BRST symmetry associated with their higher derivative structure. We first show that these theories are also invariant under a anti-BRST…
An important operation in generalized complex geometry is the Courant bracket which extends the Lie bracket that acts only on vectors to a pair given by a vector and a p-form. We explore the possibility of promoting the elements of the…
We determine the solution to the classical master equation for a 3D topological field theory with Wess-Zumino term and an underlying geometrical structure of a twisted R-Poisson manifold on its target space. The graded geometry of the…
We investigate the variation of the string field action under changes of the string field vertices giving rise to different decompositions of the moduli spaces of Riemann surfaces. We establish that any such change in the string action…
The constrained Hamiltonian analysis of geometric actions is worked out before applying the construction to the extended Bondi-Metzner-Sachs group in four dimensions. For any Hamiltonian associated with an extended BMS$_4$ generator, this…
The complete quantum theory of covariant closed strings is constructed in detail. The action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field…
This survey article is an invited contribution to the Encyclopedia of Mathematical Physics, 2nd edition. We provide an accessible overview on relevant applications of higher and derived geometry to theoretical physics, including higher…
BD algebras (Beilinson-Drinfeld algebras) are algebraic structures which are defined similarly to BV algebras (Batalin-Vilkovisky algebras). The equation defining the BD operator has the same structure as the equation for BV algebras, but…
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring…
Starting from the requirement that a Lagrangian field theory be invariant under both Schwinger-Dyson BRST and Schwinger-Dyson anti-BRST symmetry, we derive the BRST--anti-BRST analogue of the Batalin-Vilkovisky formalism. This is done…
Given a simple, simply laced, complex Lie algebra $\bfg$ corresponding to the Lie group $G$, let $\bfnp$ be the subalgebra generated by the positive roots. In this paper we construct a BV-algebra $\fA[\bfg]$ whose underlying graded…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
In this paper, we initiate the study of the Givental group action on Cohomological Field Theories in terms of homotopical algebra. More precisely, we show that the stabilisers of Topological Field Theories in genus 0 (respectively in genera…
Lecture notes for the course "Batalin-Vilkovisky formalism and applications in topological quantum field theory" given at the University of Notre Dame in the Fall 2016 for a mathematical audience. In these lectures we give a slow…
Steenrod operations have been defined by Voedvodsky in motivic cohomology in order to show the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings. The purpose of this paper is to provide…
We study the enumerative geometry of orbits of multidimensional toric action on projective algebraic varieties and develop a new cyclic differential-graded operad, conjecturally governing the real version of the enumerative geometry of…
We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz- Zaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a…