On Pure Spinor Superfield Formalism

We show that a certain superfield formalism can be used to find an off-shell supersymmetric description for some supersymmetric field theories where conventional superfield formalism does not work. This "new" formalism contains even auxiliary variables in addition to conventional odd super-coordinates. The idea of this construction is similar to the pure spinor formalism developed by N.Berkovits. It is demonstrated that using this formalism it is possible to prove that the certain Chern-Simons-like (Witten's OSFT-like) theory can be considered as an off-shell version for some on-shell supersymmetric field theories. We use the simplest non-trivial model found in [2] to illustrate the power of this pure spinor superfield formalism. Then we redo all the calculations for the case of 10-dimensional Super-Yang-Mills theory. The construction of off-shell description for this theory is more subtle in comparison with the model of [2] and requires additional Z_2 projection. We discover experimentally (through a direct explicit calculation) a non-trivial Z_2 duality at the level of Feynman diagrams. The nature of this duality requires a better investigation

Classical BV theories on manifolds with boundary

In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the $BF$ theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing.Comment: The second version has many typos corrected, references added. Some typos are probably still there, in particular, signs in examples. In the third version more typoes are corrected and the exposition is slightly change

The Poisson sigma model on closed surfaces

Using methods of formal geometry, the Poisson sigma model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections if the surface is a torus or if the Poisson structure is regular and unimodular (e.g., symplectic). In the case of a Kahler structure or of a trivial Poisson structure, the partition function on the torus is shown to be the Euler characteristic of the target; some evidence is given for this to happen more generally. The methods of formal geometry introduced in this paper might be applicable to other sigma models, at least of the AKSZ type.Comment: 32 pages; references adde