TY - JOUR

T1 - Higher spin currents with manifest S O (4) symmetry in the large = 4 holography

AU - Ahn, Changhyun

N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.

PY - 2018/12/20

Y1 - 2018/12/20

N2 - The large = 4 nonlinear superconformal algebra is generated by six spin-1 currents, four spin-3 2 currents and one spin-2 current. The simplest extension of these 11 currents is described by the 16 higher spin currents of spins (1, 3 2, 3 2, 3 2, 3 2, 2, 2, 2, 2, 2, 2, 5 2, 5 2, 5 2, 5 2, 3). In this paper, by using the defining operator product expansions (OPEs) between the 11 currents and 16 higher spin currents, we determine the 16 higher spin currents (the higher spin-1, 3 2 currents were found previously) in terms of affine Kac-Moody spin-1 2, one currents in the Wolf space coset model completely. An antisymmetric second rank tensor, three antisymmetric almost complex structures or the structure constant are contracted with the multiple product of spin-1 2, 1 currents. The eigenvalues are computed for coset representations containing at most four boxes, at finite N and k. After calculating the eigenvalues of the zeromode of the higher spin-3 current acting on the higher representations up to three (or four) boxes of Young tableaux in SU(N + 2) in the Wolf space coset, we obtain the corresponding three-point functions with two scalar operators at finite (N,k). Furthermore, under the large (N,k) 't Hooft-like limit, the eigenvalues associated with any boxes of Young tableaux are obtained and the corresponding three-point functions are written in terms of the 't Hooft coupling constant in simple form in addition to the two-point functions of scalars and the number of boxes.

AB - The large = 4 nonlinear superconformal algebra is generated by six spin-1 currents, four spin-3 2 currents and one spin-2 current. The simplest extension of these 11 currents is described by the 16 higher spin currents of spins (1, 3 2, 3 2, 3 2, 3 2, 2, 2, 2, 2, 2, 2, 5 2, 5 2, 5 2, 5 2, 3). In this paper, by using the defining operator product expansions (OPEs) between the 11 currents and 16 higher spin currents, we determine the 16 higher spin currents (the higher spin-1, 3 2 currents were found previously) in terms of affine Kac-Moody spin-1 2, one currents in the Wolf space coset model completely. An antisymmetric second rank tensor, three antisymmetric almost complex structures or the structure constant are contracted with the multiple product of spin-1 2, 1 currents. The eigenvalues are computed for coset representations containing at most four boxes, at finite N and k. After calculating the eigenvalues of the zeromode of the higher spin-3 current acting on the higher representations up to three (or four) boxes of Young tableaux in SU(N + 2) in the Wolf space coset, we obtain the corresponding three-point functions with two scalar operators at finite (N,k). Furthermore, under the large (N,k) 't Hooft-like limit, the eigenvalues associated with any boxes of Young tableaux are obtained and the corresponding three-point functions are written in terms of the 't Hooft coupling constant in simple form in addition to the two-point functions of scalars and the number of boxes.

KW - AdS/CFT

KW - extended conformal symmetry

KW - Higher spin symmetry

KW - W symmetry

UR - http://www.scopus.com/inward/record.url?scp=85059192783&partnerID=8YFLogxK

U2 - 10.1142/S0217751X18502081

DO - 10.1142/S0217751X18502081

M3 - Article

AN - SCOPUS:85059192783

SN - 0217-751X

VL - 33

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

IS - 35

M1 - 1850208

ER -