Higher Spin Currents with Arbitrary N in the N=1 Stringy Coset Minimal Model

TL;DR

This paper constructs and analyzes higher spin supercurrents in an N=1 supersymmetric coset model, deriving their operator product expansions and three-point functions for arbitrary N, revealing finite eigenvalues in the large N limit.

Contribution

It provides explicit construction of higher spin supercurrents and their OPEs for arbitrary N in the N=1 stringy coset minimal model, extending previous fixed-level results.

Findings

Derived complete nonlinear OPE of the lowest N=1 higher spin supercurrent for general N.

Calculated three-point functions involving scalar primaries and higher spin currents in the large N limit.

Showed that light states at fixed level become non-light in the large N limit due to finite eigenvalues.

Abstract

In the N=1 supersymmetric coset model based on (A_{N-1}^{(1)} \oplus A_{N-1}^{(1)}, A_{N-1}^{(1)}) at level (k, N), the lowest N=1 higher spin supercurrent with spins-(5/2, 3), in terms of two independent numerator WZW currents, is reviewed. By calculating the operator product expansions (OPE) between this N=1 higher spin supercurrent and itself, the next two N=1 higher spin supercurrents can be generated with spins-(7/2, 4) and (4, 9/2). These four currents are polynomials of degree 3, 4, 4, 4 in the first numerator WZW currents with level k. The complete nonlinear OPE of the lowest N=1 higher spin supercurrent for general N is obtained. The three-point functions involving two scalar primaries with one spin-2 current or spin-3 current are calculated in the large N limit for all values of the 't Hooft coupling. In particular, the light states that appeared in the case when the second level was fixed by 1 are no longer light ones because the eigenvalues are finite in the large N limit.