https://doi.org/10.1140/epjc/s10052-021-09858-3
Regular Article - Theoretical Physics
Adding complex fermions to the Grassmannian-like coset model
Department of Physics, Kyungpook National University, 41566, Daegu, Korea
Received:
21
July
2021
Accepted:
21
November
2021
Published online:
22
December
2021
In the 
supersymmetric coset model, 
, we construct the SU(M) nonsinglet multiplet of spins 
in terms of coset fields. The next SU(M) singlet and nonsinglet multiplets of spins 
are determined by applying the supersymmetry currents of spin 
to the bosonic singlet and nonsinglet currents of spin 3 in the bosonic coset model. We also obtain the operator product expansions (OPEs) between the currents of the superconformal algebra and above three kinds of multiplets. These currents in two dimensions play the role of the asymptotic symmetry, as the generators of “rectangular W-algebra”, of the 
matrix generalization of 
higher spin theory in the bulk. The structure constants in the right hand sides of these OPEs are dependent on the three parameters k, N and M explicitly. Moreover, the OPEs between SU(M) nonsinglet multiplet of spins and itself are analyzed in detail. The complete OPE between the lowest component of the SU(M) singlet multiplet of spins and itself is described. In particular, when 
, it is known that the above supersymmetric coset model provides the realization of the extension of the large 
nonlinear superconformal algebra. We determine the currents of the large nonlinear superconformal algebra and the higher spin-
currents of the lowest multiplet for generic k and N in terms of the coset fields. For the remaining higher spin-
currents of the lowest 
multiplet, some of the results are given.
© The Author(s) 2021
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