A supersymmetric enhancement of N $$ \mathcal{N} $$ = 1 holographic minimal model
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Springer
Received: February 14, 2019 Accepted: May 6, 2019 Published: May 22, 2019
Changhyun Ahn and Jinsub Paeng Department of Physics, Kyungpook National University, 80 Dae-Hak-Ro Buk-Gu, Taegu 41566, South Korea
E-mail: [email protected], [email protected] Abstract: By studying the N = 1 holographic minimal model at the “critical” level, we obtain the lowest N = 2 higher spin multiplet of spins 32 , 2, 2, 52 in terms of two adjoint fermion types for generic N . We subsequently determine operator product expansions between the lowest and second lowest (N = 2) higher spin multiplet of spins 3, 27 , 72 , 4 , and the corresponding Vasiliev’s oscillator formalism with matrix generalization on AdS3 higher spin theory in the extension of OSp(2|2) superconformal algebra. Under the large N limit (equivalent to large central charge) in the extension of N = 2 superconformal algebra in two dimensions, operator product expansions provide asymptotic symmetry algebra in AdS3 higher spin theory. Keywords: AdS-CFT Correspondence, Conformal and W Symmetry, Higher Spin Gravity, Higher Spin Symmetry ArXiv ePrint: 1902.03699
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)135
JHEP05(2019)135
A supersymmetric enhancement of N = 1 holographic minimal model
Contents 1 Introduction
2
2 Four currents for N = 2 superconformal algebra 2.1 Kac-Moody spin-1 currents 2.2 Four currents in terms of fermions
4 4 5 6 6 9 10
4 Operator product expansions between N = 2 higher spin multiplets 4.1 First N = 2 higher spin multiplet for generic N 4.2 Operator product expansion between the first N = 2 higher spin multiplet 4.3 Operator product expansions between first and second N = 2 higher spin multiplets
12 12 13
5 AdS3 higher spin theory with matrix generalization 5.1 Wedge algebra for N = 2 superconformal algebra 5.2 OSp(2|2) higher spin algebra 5.2.1 Twelve higher spin generators 5.2.2 Next twenty-four higher spin generators
16 17 18 18 19
6 Conclusions
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A N = 2 superconformal algebra
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15
B Operator product expansions between the four currents and higher spin currents 23 C Remaining operator product expansions for section 4.2
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D Quasi primary operators from section 4.3
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E Operator product expansions between N = 2 higher spin multiplets in (4.1) E.1 Operator product expansions between the first and third N = 2 higher spin multiplets E.2 Operator product expansions between the second N = 2 higher spin multiplet E.3 Operator product expansions between the second and the third N = 2 higher spin multiplets E.4 Operator product expansions between the third N = 2 higher spin multiplet F Partners for (5.13) from section 5.2
–1–
29 29 30 32 33 36
JHEP05(2019)135
3 N = 2 higher spin currents for fixed N = 4 3.1 The first (lowest) N = 2 higher spin multiplet 3.2 Second N = 2 higher spin multiplet 3.3 Third and fourth N = 2 higher spin multiplets
1
Introduction
c c G SO(2N + 1)k ⊕ SO(2N )1 with k = 2N − 1. = c H SO(2N )k+1
(1.1)
For SO(2N +1), the quadratic Casimir eigenvalue
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