On Pure Spinor Superfield Formalism

TL;DR

This paper introduces a superfield formalism inspired by pure spinors that provides off-shell supersymmetric descriptions for certain theories where traditional methods fail, demonstrated through models like 10D Super-Yang-Mills.

Contribution

It develops a novel pure spinor superfield formalism with auxiliary variables, enabling off-shell formulations of supersymmetric theories previously inaccessible by standard superfield approaches.

Findings

Successfully applied to a Chern-Simons-like theory as an off-shell model.

Constructed off-shell description for 10D Super-Yang-Mills theory.

Discovered a non-trivial Z_2 duality at the diagram level.

Abstract

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.