A Charged and Neutral Spin-$4$ Currents in the Grassmannian-like Coset Model

TL;DR

This paper constructs primary charged and neutral spin-4 currents in a Grassmannian-like coset model by analyzing operator product expansions, revealing their algebraic structure and parameter dependence.

Contribution

It explicitly determines primary spin-4 currents from OPE calculations and explores their relations with lower spin currents in the model.

Findings

Primary charged and neutral spin-4 currents are identified in the OPEs.

The primary spin-4 currents appear at specific poles in the OPEs for generic parameters.

The large k limit of the OPEs is also analyzed.

Abstract

By calculating the second order pole in the operator product expansion (OPE) of the charged spin-$3$ current with the neutral spin-$3$ current in the Grassmannian-like coset model, we determine the primary charged spin-$4$ current. Similarly, by computing the second order pole in the OPE of the neutral spin-$3$ current with itself, we obtain the primary neutral spin-$4$ current. We determine the OPE of the charged spin-$2$ current with the charged spin-$3$ current for generic parameters and the large $k$ (one of the parameters) limit is also obtained for this OPE. In particular, the above primary charged spin-$4$ current appears in the first order pole of this OPE for generic parameters. We also check that the above primary charged and neutral spin-$4$ currents occur at the second order pole in the OPE of the charged spin-$3$ current with itself for fixed parameters.