Download PDF

Higher spin currents in the holographic \( \mathcal{N} \) = 1 coset minimal model

Open Access
Article
First Online:
Received:
Accepted:

Abstract

In the \( \mathcal{N} \) = 1 supersymmetric coset minimal model based on \( \left( {B_N^{(1)}\oplus D_N^{(1) },\ D_N^{(1) }} \right) \) at level (k, 1) studied recently, the standard \( \mathcal{N} \) = 1 super stress tensor of spins \( \left( {\frac{3}{2},2} \right) \) is reviewed. By considering the stress tensor in the coset \( \left( {B_N^{(1) },\ D_N^{(1) }} \right) \) at level k, the higher spin-2′ Casimir current was obtained previously. By acting the above spin- \( \frac{2}{3} \) current on the higher spin-2′ Casimir current, its superpartner, the higher spin- \( \frac{5}{2} \) current, can be generated and combined as the first higher spin supercurrent with spins \( \left( {{2^{\prime }},\frac{5}{2}} \right) \). By calculating the operator product expansions (OPE) between the higher spin supercurrent and itself, the next higher spin supercurrent can be generated with spins \( \left( {\frac{7}{2},4} \right) \). Moreover, the other higher spin supercurrent with spins \( \left( {{4^{\prime }},\frac{9}{2}} \right) \) can be generated by calculating the OPE between the first higher spin supercurrent with spins \( \left( {{2^{\prime }},\frac{5}{2}} \right) \) and the second higher spin supercurrent with spins \( \left( {\frac{7}{2},\ 4} \right) \). Finally, the higher spin supercurrent, \( \left( {\frac{11 }{2},6} \right) \), can be extracted from the right hand side of OPE between the higher spin supercurrents, \( \left( {{2^{\prime }},\frac{5}{2}} \right) \) and \( \left( {{4^{\prime }},\frac{9}{2}} \right) \).

Keywords

AdS-CFT Correspondence Conformal and W Symmetry 
Download to read the full article text

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    M.R. Gaberdiel and R. Gopakumar, An AdS 3 dual for minimal model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].ADSGoogle Scholar
  2. [2]
    M.R. Gaberdiel and R. Gopakumar, Triality in minimal model holography, JHEP 07 (2012) 127 [arXiv:1205.2472] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  3. [3]
    C. Ahn, The large-N ’t Hooft limit of coset minimal models, JHEP 10 (2011) 125 [arXiv:1106.0351] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    M.R. Gaberdiel and C. Vollenweider, Minimal model holography for SO(2N), JHEP 08 (2011) 104 [arXiv:1106.2634] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  5. [5]
    T. Creutzig, Y. Hikida and P.B. Rønne, N = 1 supersymmetric higher spin holography on AdS 3, JHEP 02 (2013) 019 [arXiv:1209.5404] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    S. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    C. Candu and C. Vollenweider, The \( \mathcal{N} \) = 1 algebra \( {{\mathcal{W}}_{\infty }}\left[ \mu \right] \) and its truncations, JHEP 11 (2013) 032 [arXiv:1305.0013] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    C. Ahn, The primary Spin-4 Casimir operators in the holographic SO(N) coset minimal models, JHEP 05 (2012) 040 [arXiv:1202.0074] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    P. Bowcock, Quasi-primary fields and associativity of chiral algebras, Nucl. Phys. B 356 (1991) 367 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    R. Blumenhagen et al., W algebras with two and three generators, Nucl. Phys. B 361 (1991) 255 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    P. Bouwknegt and K. Schoutens, W symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [hep-th/9210010] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    W. Nahm, Algebras of two-dimensional chiral fields and their classification, in Proceedings, Mathematical physics, Islamabad Pakistan (1989), pg. 283 [INSPIRE].
  13. [13]
    W. Nahm, Chiral algebras of two-dimensional chiral field theories and their normal ordered products, in Proceedings, Recent developments in conformal field theories, Trieste Italy (1989), pg. 81 [INSPIRE].
  14. [14]
    K. Thielemans, A mathematica package for computing operator product expansions, Int. J. Mod. Phys. C 2 (1991) 787 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  15. [15]
    C. Candu, M.R. Gaberdiel, M. Kelm and C. Vollenweider, Even spin minimal model holography, JHEP 01 (2013) 185 [arXiv:1211.3113] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    C. Ahn and J. Paeng, The OPEs of Spin-4 Casimir currents in the holographic SO(N) coset minimal models, Class. Quant. Grav. 30 (2013) 175004 [arXiv:1301.0208] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  17. [17]
    D. Friedan, E.J. Martinec and S.H. Shenker, Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    C. Ahn, The higher spin currents in the N = 1 stringy coset minimal model, JHEP 04 (2013) 033 [arXiv:1211.2589] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    C. Ahn, The coset Spin-4 Casimir operator and its three-point functions with scalars, JHEP 02 (2012) 027 [arXiv:1111.0091] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    C. Ahn and H. Kim, Spin-5 Casimir operator and its three-point functions with two scalars, arXiv:1308.1726 [INSPIRE].
  21. [21]
    M.R. Gaberdiel and R. Gopakumar, Large \( \mathcal{N} \) = 4 holography, JHEP 09 (2013) 036 [arXiv:1305.4181] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    C. Ahn, The large-N ’t Hooft limit of Kazama-Suzuki model, JHEP 08 (2012) 047 [arXiv:1206.0054] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    C. Ahn, The operator product expansion of the lowest higher spin current at finite N, JHEP 01 (2013) 041 [arXiv:1208.0058] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    T. Creutzig, Y. Hikida and P.B. Ronne, Extended higher spin holography and Grassmannian models, JHEP 11 (2013) 038 [arXiv:1306.0466] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    C. Ahn, Higher spin currents with arbitrary N in the \( \mathcal{N} \) = ∞ stringy coset minimal model, JHEP 07 (2013) 141 [arXiv:1305.5892] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Dept. of PhysicsKyungpook National UniversityTaeguSouth Korea

Personalised recommendations