1211.2589 (Changhyun Ahn)

The Higher Spin Currents in the N=1 Stringy Coset Minimal Model    [PDF]

Changhyun Ahn

We reconsider the N=1 supersymmetric extension of W_3 algebra which was studied previously. This consists of seven higher spin supercurrents (fourteen higher spin currents in components) as well as the N=1 stress energy tensor of spins (3/2, 2). So far, the complete expressions for the higher spin currents are not known. In this paper, we construct them explicitly both in the c=4 eight free fermion model and in the supersymmetric coset model based on (A_2^{(1)} \oplus A_2^{(1)}, A_2^{(1)}) at level (3,k). By acting the above spin-3/2 current on the higher spin-3 Casimir current, one generates its fermionic partner, the higher spin-5/2 current and they can be combined as a first higher spin supercurrent with spins (5/2, 3). Then by computing the operator product expansions(OPE) between the higher spin supercurrent and itself, one can generate the next two higher spin supercurrents with spins (7/2, 4) and (4, 9/2). Moreover, the other two higher spin supercurrents with spins (4, 9/2) and (9/2, 5) are generated by calculating the OPE between the first higher spin supercurrent with spins (5/2, 3) and the second higher spin supercurrent with spins (7/2, 4). Finally, the remaining two higher spin supercurrents with spins (11/2, 6) and (6, 13/2), from the first higher spin supercurrent and the fourth higher spin supercurrent with spins (4, 9/2), are obtained similarly.

View original: http://arxiv.org/abs/1211.2589