The 𝒩 = 4 coset model and the higher spin algebra
Abstract
By computing the operator product expansions between the first two 𝒩 = 4 higher spin multiplets in the unitary coset model, the (anti-)commutators of higher spin currents are obtained under the large (N,k) ’t Hooft-like limit. The free field realization with complex bosons and fermions is presented. The (anti-)commutators for generic spins s1 and s2 with manifest SO(4) symmetry at vanishing ’t Hooft-like coupling constant are completely determined. The structure constants can be written in terms of the ones in the 𝒩 = 2 𝒲∞ algebra found by Bergshoeff, Pope, Romans, Sezgin and Shen previously, in addition to the spin-dependent fractional coefficients and two SO(4) invariant tensors. We also describe the 𝒩 = 4 higher spin generators, by using the above coset construction results, for general superspin 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.
- Publication:
-
International Journal of Modern Physics A
- Pub Date:
- April 2020
- DOI:
- 10.1142/S0217751X20500463
- arXiv:
- arXiv:1910.02183
- Bibcode:
- 2020IJMPA..3550046A
- Keywords:
-
- AdS/CFT;
- higher spin theory;
- W symmetry;
- coset model;
- 11.25.Hf;
- 11.25.Tq;
- Conformal field theory algebraic structures;
- Gauge/string duality;
- High Energy Physics - Theory
- E-Print:
- 99 pages