Higher spin currents in the N=2 stringy coset minimal model

Abstract

In the coset model based on (A_{N-1}^{(1)} \oplus A_{N-1}^{(1)}, A_{N-1}^{(1)}) at level (N, N; 2N), it is known that the N=2 superconformal algebra can be realized by the two kinds of adjoint fermions. Each Kac-Moody current of spin-1 is given by the product of fermions with structure constant (f symbols) as usual. One can construct the spin-1 current by combining the above two fermions with the structure constant and the spin-1 current by multiplying these two fermions with completely symmetric SU(N) invariant tensor of rank 3 (d symbols). The lowest higher spin-2 current with nonzero U(1) charge (corresponding to the zeromode eigenvalue of spin-1 current of N=2 superconformal algebra) can be obtained from these four spin-1 currents in quadratic form. Similarly, the other type of lowest higher spin-2 current, whose U(1) charge is opposite to the above one, can be obtained also. Four higher spin-5/2 currents can be constructed from the operator product expansions (OPEs) between the spin-3/2 currents of N=2 superconformal algebra and the above two higher spin-2 currents. The two higher spin-3 currents can be determined by the OPEs between the above spin-3/2 currents and the higher spin-5/2 currents. Finally, the ten N=2 OPEs between the four N=2 higher spin multiplets (2, 5/2, 5/2, 3), (2, 5/2, 5/2, 3), (7/2, 4, 4, 9/2) and (7/2, 4, 4, 9/2) are obtained explicitly for generic N.