The Operator Product Expansions in the N=4 Coset Model

by Man Hea Kim (Ph.D Candidate)

Wednesday Nov 27, 2019, 2:00 PM → 3:00 PM Asia/Seoul

119호 (제1과학관)

We construct the higher spin currents, which are components of the low super spin muti- plet, in the N = 4 superconformal Wolf space coset SU(N+2) / SU(N)×SU(2)×U(1) (Unitary) and  SO(N+4) / SO(N)×SO(4) (Orthgonal), respectively. The OPEs between these higher spin currents can be obtained in the calculation of the N = 1 Affine Kac-Moody current of the coset theories. From the infor- mation of these OPEs, we can compare the spectrum of higher spin current appearing in the OPEs between the Unitary and the Orthogonal coset model. There exist SO(4) adjoint and SO(4) vector higher spin multiplets in the Orthgonal coset model, unlike exist only SO(4) siglet higher spin in the Unitary model.
By careful analysis of the zero mode (higher spin) eigenvalue equations, the three-point functions of bosonic higher spin 2, 3, 4 currents with two scalars are obtained for finite N and k in the unitary coset model. Furthermore, we also analyze the three-point functions of bosonic higher spin 2, 3, 4 currents in the extension of the large N = 4 linear superconformal algebra.
By computing the OPEs in the unitary coset model, the (anti)commutators of higher spin currents are obtained under the large (N;k) ’t Hooft-like limit. From the commutator, we find exact relations of the higher spin fields between the N = 4 unitary coset model, the free field realization and the deformed oscillator algebra. We describe the N = 4 higher spin generators, by using the above relations, for general super spin s in terms of oscillators in the matrix generalization of AdS3 Vasiliev higher spin theory at nonzero ’t Hooft-like coupling constant. We obtain the N = 4 higher spin algebra for low spins and present how to determine the structure constants, which depend on the higher spin algebra parameter, in general, for fixed spins s1 and s2.

Thesis Advisor: Prof. Changhyun Ahn