TY - JOUR
T1 - The Grassmannian-like coset model and the higher spin currents
AU - Ahn, Changhyun
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/3
Y1 - 2021/3
N2 - In the Grassmannian-like coset model, SU(N+M)kSU(N)k×U(1)kNM(N+M), Creutzig and Hikida have found the charged spin-2, 3 currents and the neutral spin-2, 3 currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-2 current and itself, the OPE between the charged spin-2 current and the charged spin-3 current and the OPE between the neutral spin-3 current and itself for generic N, M and k. From the second OPE, we obtain the new charged quasi primary spin-4 current while from the last one, the new neutral primary spin-4 current is found implicitly. The infinity limit of k in the structure constants of the OPEs is described in the context of asymptotic symmetry of M×M matrix generalization of AdS3 higher spin theory. Moreover, the OPE between the charged spin-3 current and itself is determined for fixed (N, M) = (5, 4) with arbitrary k up to the third order pole. We also obtain the OPEs between charged spin-1, 2, 3 currents and neutral spin-3 current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-4 current in the second order pole for fixed (N, M) = (5, 4). We comment on the complex free fermion realization.
AB - In the Grassmannian-like coset model, SU(N+M)kSU(N)k×U(1)kNM(N+M), Creutzig and Hikida have found the charged spin-2, 3 currents and the neutral spin-2, 3 currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-2 current and itself, the OPE between the charged spin-2 current and the charged spin-3 current and the OPE between the neutral spin-3 current and itself for generic N, M and k. From the second OPE, we obtain the new charged quasi primary spin-4 current while from the last one, the new neutral primary spin-4 current is found implicitly. The infinity limit of k in the structure constants of the OPEs is described in the context of asymptotic symmetry of M×M matrix generalization of AdS3 higher spin theory. Moreover, the OPE between the charged spin-3 current and itself is determined for fixed (N, M) = (5, 4) with arbitrary k up to the third order pole. We also obtain the OPEs between charged spin-1, 2, 3 currents and neutral spin-3 current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-4 current in the second order pole for fixed (N, M) = (5, 4). We comment on the complex free fermion realization.
KW - AdS-CFT Correspondence
KW - Conformal and W Symmetry
KW - Higher Spin Gravity
KW - Higher Spin Symmetry
UR - http://www.scopus.com/inward/record.url?scp=85102108198&partnerID=8YFLogxK
U2 - 10.1007/JHEP03(2021)037
DO - 10.1007/JHEP03(2021)037
M3 - Article
AN - SCOPUS:85102108198
SN - 1029-8479
VL - 2021
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 3
M1 - 37
ER -