Unitarity, crossing symmetry and duality of the S-matrix in large N Chern-Simons theories with fundamental matter

  • Sachin Jain
  • Mangesh Mandlik
  • Shiraz Minwalla
  • Tomohisa Takimi
  • Spenta R. Wadia
  • Shuichi Yokoyama
Open Access
Regular Article - Theoretical Physics

Abstract

We present explicit computations and conjectures for 2 → 2 scattering matrices in large N U(N ) Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the ’t Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non-analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.

Keywords

Duality in Gauge Field Theories Chern-Simons Theories 1/N Expansion Sigma Models 

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]
    S. Giombi et al., Chern-Simons theory with vector fermion matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    O. Aharony, G. Gur-Ari and R. Yacoby, D = 3 bosonic vector models coupled to Chern-Simons gauge theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  4. [4]
    J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    O. Aharony, G. Gur-Ari and R. Yacoby, Correlation functions of large-N Chern-Simons-matter theories and bosonization in three dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    G. Gur-Ari and R. Yacoby, Correlators of large-N Fermionic Chern-Simons vector models, JHEP 02 (2013) 150 [arXiv:1211.1866] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    S. Jain, S.P. Trivedi, S.R. Wadia and S. Yokoyama, Supersymmetric Chern-Simons theories with vector matter, JHEP 10 (2012) 194 [arXiv:1207.4750] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    O. Aharony, S. Giombi, G. Gur-Ari, J. Maldacena and R. Yacoby, The thermal free energy in large-N Chern-Simons-matter theories, JHEP 03 (2013) 121 [arXiv:1211.4843] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    S. Jain et al., Phases of large-N vector Chern-Simons theories on S 2 × S 1, JHEP 09 (2013) 009 [arXiv:1301.6169] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    T. Takimi, Duality and higher temperature phases of large-N Chern-Simons matter theories on S 2 × S 1, JHEP 07 (2013) 177 [arXiv:1304.3725] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    A. Giveon and D. Kutasov, Seiberg duality in Chern-Simons theory, Nucl. Phys. B 812 (2009) 1 [arXiv:0808.0360] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities, JHEP 10 (2011) 075 [arXiv:1108.5373] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    S. Jain, S. Minwalla and S. Yokoyama, Chern-Simons duality with a fundamental boson and fermion, JHEP 11 (2013) 037 [arXiv:1305.7235] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    D. Bak, R. Jackiw and S.-Y. Pi, Non-Abelian Chern-Simons particles and their quantization, Phys. Rev. D 49 (1994) 6778 [hep-th/9402057] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ triality: from higher spin fields to strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  16. [16]
    S.N.M. Ruijsenaars, The Aharonov-Bohm effect and scattering theory, Annals Phys. 146 (1983) 1 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    S. Yokoyama, A note on large-N thermal free energy in supersymmetric Chern-Simons vector models, JHEP 01 (2014) 148 [arXiv:1310.0902] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  18. [18]
    Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115 (1959) 485 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    R. Jackiw, Dynamical symmetry of the magnetic vortex, Annals Phys. 201 (1990) 83 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    D. Bak and O. Bergman, Perturbative analysis of non-Abelian Aharonov-Bohm scattering, Phys. Rev. D 51 (1995) 1994 [hep-th/9403104] [INSPIRE].ADSGoogle Scholar
  21. [21]
    G. Amelino-Camelia and D. Bak, Schrödinger selfadjoint extension and quantum field theory, Phys. Lett. B 343 (1995) 231 [hep-th/9406213] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    C. Nayak, S.H. Simon, A. Stern, M. Freedman and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80 (2008) 1083 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    A. Agarwal, N. Beisert and T. McLoughlin, Scattering in mass-deformed N ≥ 4 Chern-Simons models, JHEP 06 (2009) 045 [arXiv:0812.3367] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    T. Bargheer, N. Beisert, F. Loebbert and T. McLoughlin, Conformal anomaly for amplitudes in N = 6 superconformal Chern-Simons theory, J. Phys. A 45 (2012) 475402 [arXiv:1204.4406] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  26. [26]
    M.S. Bianchi, M. Leoni, A. Mauri, S. Penati and A. Santambrogio, Scattering in ABJ theories, JHEP 12 (2011) 073 [arXiv:1110.0738] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    W.-M. Chen and Y.-T. Huang, Dualities for loop amplitudes of N = 6 Chern-Simons matter theory, JHEP 11 (2011) 057 [arXiv:1107.2710] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    M.S. Bianchi, M. Leoni, A. Mauri, S. Penati and A. Santambrogio, Scattering amplitudes/Wilson loop duality in ABJM theory, JHEP 01 (2012) 056 [arXiv:1107.3139] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    M.S. Bianchi and M. Leoni, On the ABJM four-point amplitude at three loops and BDS exponentiation, JHEP 11 (2014) 077 [arXiv:1403.3398] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    M.S. Bianchi, M. Leoni, A. Mauri, S. Penati and A. Santambrogio, One loop amplitudes in ABJM, JHEP 07 (2012) 029 [arXiv:1204.4407] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    W.L. van Neerven and J.A.M. Vermaseren, Large loop integrals, Phys. Lett. B 137 (1984) 241 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    G. ’t Hooft and M.J.G. Veltman, Scalar one loop integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    G. Passarino and M.J.G. Veltman, One loop corrections for e + e annihilation into μ + μ in the Weinberg model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated one loop integrals, Phys. Lett. B 302 (1993) 299 [Erratum ibid. B 318 (1993) 649] [hep-ph/9212308] [INSPIRE].
  35. [35]
    G. ’t Hooft and M. Veltman, Diagrammar, NATO Adv. Study Inst. Ser. B Phys. 4 (1974) 177 [INSPIRE].Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Sachin Jain
    • 1
  • Mangesh Mandlik
    • 1
  • Shiraz Minwalla
    • 1
    • 2
  • Tomohisa Takimi
    • 3
  • Spenta R. Wadia
    • 1
    • 4
  • Shuichi Yokoyama
    • 1
  1. 1.Department of Theoretical PhysicsTata Institute of Fundamental ResearchMumbaiIndia
  2. 2.School of Natural SciencesInstitute for Advanced StudyPrincetonUnited States
  3. 3.Harish-Chandra Research InstituteAllahabadIndia
  4. 4.International Centre for Theoretical Sciences, Tata Institute of Fundamental ResearchTIFR Centre Building, Indian Institute of ScienceBangaloreIndia

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