Journal of High Energy Physics

, 2017:153 | Cite as

Self-consistency of conformally coupled ABJM theory at the quantum level

Open Access
Regular Article - Theoretical Physics
  • 31 Downloads

Abstract

We study the \( \mathcal{N} \) = 6 superconformal Chern-Simons matter field theory (the ABJM theory) conformally coupled to a Lorentzian, curved background spacetime. To support rigid supersymmetry, such backgrounds have to admit twistor spinors. At the classical level, the symmetry of the theory can be described by a conformal symmetry superalgebra. We show that the full \( \mathcal{N} \) = 6 superconformal algebra persists at the quantum level using the BV-BRST method.

Keywords

Anomalies in Field and String Theories BRST Quantization Chern-Simons Theories Supersymmetric Gauge Theory 

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]
    G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    B. Jia and E. Sharpe, Rigidly Supersymmetric Gauge Theories on Curved Superspace, JHEP 04 (2012) 139 [arXiv:1109.5421] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    H. Samtleben and D. Tsimpis, Rigid supersymmetric theories in 4d Riemannian space, JHEP 05 (2012) 132 [arXiv:1203.3420] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    C. Klare, A. Tomasiello and A. Zaffaroni, Supersymmetry on Curved Spaces and Holography, JHEP 08 (2012) 061 [arXiv:1205.1062] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    T.T. Dumitrescu, G. Festuccia and N. Seiberg, Exploring Curved Superspace, JHEP 08 (2012) 141 [arXiv:1205.1115] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    D. Cassani, C. Klare, D. Martelli, A. Tomasiello and A. Zaffaroni, Supersymmetry in Lorentzian Curved Spaces and Holography, Commun. Math. Phys. 327 (2014) 577 [arXiv:1207.2181] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    J.T. Liu, L.A. Pando Zayas and D. Reichmann, Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity, JHEP 10 (2012) 034 [arXiv:1207.2785] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    T.T. Dumitrescu and G. Festuccia, Exploring Curved Superspace (II), JHEP 01 (2013) 072 [arXiv:1209.5408] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    A. Kehagias and J.G. Russo, Global Supersymmetry on Curved Spaces in Various Dimensions, Nucl. Phys. B 873 (2013) 116 [arXiv:1211.1367] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    K. Hristov, A. Tomasiello and A. Zaffaroni, Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black Hole Holography, JHEP 05 (2013) 057 [arXiv:1302.5228] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    D. Martelli, A. Passias and J. Sparks, The supersymmetric NUTs and bolts of holography, Nucl. Phys. B 876 (2013) 810 [arXiv:1212.4618] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    P. de Medeiros and S. Hollands, Conformal symmetry superalgebras, Class. Quant. Grav. 30 (2013) 175016 [arXiv:1302.7269] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    A. Pini, D. Rodriguez-Gomez and J. Schmude, Rigid Supersymmetry from Conformal Supergravity in Five Dimensions, JHEP 09 (2015) 118 [arXiv:1504.04340] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    N. Maggiore, Algebraic renormalization of N = 2 super Yang-Mills theories coupled to matter, Int. J. Mod. Phys. A 10 (1995) 3781 [hep-th/9501057] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    L. Baulieu and G. Bossard, Superconformal invariance from N = 2 supersymmetry Ward identities, JHEP 02 (2008) 075 [arXiv:0711.3776] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    P.L. White, Analysis of the superconformal cohomology structure of N = 4 super Yang-Mills, Class. Quant. Grav. 9 (1992) 413 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    L. Baulieu and G. Bossard, Supersymmetric renormalization prescription in N = 4 super-Yang-Mills theory, Phys. Lett. B 643 (2006) 294 [hep-th/0609189] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    P. de Medeiros and S. Hollands, Superconformal quantum field theory in curved spacetime, Class. Quant. Grav. 30 (2013) 175015 [arXiv:1305.0499] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    R. Brunetti, K. Fredenhagen and M. Kohler, The Microlocal spectrum condition and Wick polynomials of free fields on curved space-times, Commun. Math. Phys. 180 (1996) 633 [gr-qc/9510056] [INSPIRE].
  21. [21]
    R. Brunetti and K. Fredenhagen, Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds, Commun. Math. Phys. 208 (2000) 623 [math-ph/9903028] [INSPIRE].
  22. [22]
    S. Hollands and R.M. Wald, Local Wick polynomials and time ordered products of quantum fields in curved space-time, Commun. Math. Phys. 223 (2001) 289 [gr-qc/0103074] [INSPIRE].
  23. [23]
    S. Hollands and R.M. Wald, Existence of local covariant time ordered products of quantum fields in curved space-time, Commun. Math. Phys. 231 (2002) 309 [gr-qc/0111108] [INSPIRE].
  24. [24]
    S. Hollands and R.M. Wald, On the renormalization group in curved space-time, Commun. Math. Phys. 237 (2003) 123 [gr-qc/0209029] [INSPIRE].
  25. [25]
    S. Hollands, Renormalized Quantum Yang-Mills Fields in Curved Spacetime, Rev. Math. Phys. 20 (2008) 1033 [arXiv:0705.3340] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    M.T. Tehrani, Quantum BRST charge in gauge theories in curved space-time, arXiv:1703.04148 [INSPIRE].
  27. [27]
    H. Baum and F. Leitner, The twistor equation in lorentzian spin geometry, Math. Z. 247 (2004) 795. [math/0305063].
  28. [28]
    H. Baum, Conformal Killing spinors and special geometric structures in Lorentzian geometry: A Survey, math/0202008 [INSPIRE].
  29. [29]
    H. Baum, Holonomy groups of lorentzian manifolds: a status report, in Global differential geometry, pg. 163-200, Springer (2012).Google Scholar
  30. [30]
    F. Leitner, Conformal killing forms with normalisation condition, in Proceedings of the 24th Winter School “Geometry and Physics”, pg. 279, Circolo Matematico di Palermo (2005).Google Scholar
  31. [31]
    H. Baum, Conformal killing spinors and the holonomy problem in lorentzian geometry — a survey of new results, in Symmetries and overdetermined systems of partial differential equations, pg. 251-264, Springer (2008).Google Scholar
  32. [32]
    P. Jordan, J. Ehlers and W. Kundt, Republication of: Exact solutions of the field equations of the general theory of relativity, Gen. Rel. Grav. 41 (2009) 2191.ADSMathSciNetCrossRefMATHGoogle Scholar
  33. [33]
    H.W. Brinkmann, Einstein spapces which are mapped conformally on each other, Math. Ann. 94 (1925) 119 [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    M.A. Bandres, A.E. Lipstein and J.H. Schwarz, Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry, JHEP 09 (2008) 027 [arXiv:0807.0880] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press (1992).Google Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany
  2. 2.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany

Personalised recommendations