The BRS Cohomology of the Wess Zumino Chiral Scalar supersymmetric model with exotic pairs and exotic triplets (E2)

TL;DR

This paper explores the BRS cohomology of the Wess Zumino supersymmetric model, introducing new invariants called exotic pairs and triplets through spectral sequence methods, revealing complex structures and potential anomalies.

Contribution

It extends the BRS cohomology analysis by including sources for field variations, leading to the discovery of new invariants and anomalies called exotic pairs and triplets.

Findings

Identifies new invariants at dimension zero called exotic pairs.

Introduces a new ghost charge -1 term called an exotic triplet.

Analyzes BRS cohomology for low spins and dimensions.

Abstract

Using the spectral sequence method, this paper advances some of the construction of the BRS cohomology of the Wess Zumino supersymmetric action. An important missing part was the inclusion of the sources for the variations of the fields. In this paper, these sources are called pseudofields. Since the most interesting part of the result contains unsaturated spinor indices, we include a constant spinor to saturate those indices. At dimension zero, this gives rise to a new set of invariants and a closely related new set of possible supersymmetry anomalies in the theory, and we call this an `exotic pair'. At dimension one, this becomes more complicated, and the theory adds a new ghost charge - 1 term, which we call a change, and we call this an `exotic triplet'. For higher dimension and higher spin, it appears that more complications are likely to occur. These exotic pairs and triplets are constrained by some simple equations which arise from the spectral sequence. The invariants of the exotic pairs are all dependent on the pseudofields, which means that the field parts of these invariants are not supersymmetric, though the invariants are in the cohomology space of supersymmetry. In this paper we examine the BRS cohomology for low spins and low dimensions.