The Hochschild-Kostant-Rosenberg theorem relates negative cyclic homology of the functions on a differential graded manifold M to the de Rham complex of M. The natural A-infinity structure on negative cyclic homology corresponds to an A-infinity structure on the de Rham complex called the Fedosov product. (This product agrees with the usual one if either argument is closed, but it is not...
I will introduce classical and quantum "thick morphisms" of supermanifolds. These are differential-geometric constructions that provide L-infinity morphisms for homotopy analogs of Poisson brackets; in particular, for homotopy brackets generated by higher-order Batalin-Vilkovisky type operators. They generalize ordinary smooth maps of supermanifolds with pullbacks on functions that are non-linear maps.
Motivated by the problem of giving a Hamiltonian description of nonlocal field theories such as string field theory, we propose a formula for the phase space symplectic structure of a generic Lagrangian field theory expressed in BV form.
In the BV formalism the spaces of fields are presented as complexes whose cohomology returns the physical content. Different but equivalent complexes may be used, which turns out to be important conceptually and in practice. One useful operation is that of a partial integration (BV pushforward), which produces a chain map that, under some assumptions, is a quasiisomorphism. This has several...
We discuss BV quantization that arises from topologically/holomorphically twisted quantum field theory. We illustrate some applications in topological/chiral algebraic index, topological B-model and mirror symmetry.
I will review recent progress on understanding perturbative quantum field theory within the realm of homotopy algebras.
In Witten's CS/WZW correspondence the chiral WZW model appears from the chiral boundary condition imposed on the CS theory.
I will describe how similar boundary conditions (mixed chiral-antichiral) of the CS theory and of its AKSZ analogs produce many other interesting examples and how they explain, in particular, Poisson-Lie T-duality. Unlike the CS/WZW correspondence, this generalization is...
The BRST quantisation of the relativistic spinning particle pulls the path integral back to ist (super) moduli space and thereby interpolates between the space-time BV action and the BV-equation on super moduli space. This is perhaps the simplest toy model of super string field theory.
We first review how one can turn the standard sigma model in
to a gauge theory and under what conditions. This leads us to the notion
of singular Riemannian foliations (SRFs) and equivalence of gauge
theories leads to Morita equivalence of SRFs. This leads one looking at
the octonionic singular foliation on R^16. In this talk we provide a Lie
groupoid generating this foliation and show...
