Skip to main content
SpringerLink
Log in

Form factors of chiral primary operators at two loops in ABJ(M)

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We calculate the colour-ordered form factor for chiral primary operators built from J scalar fields of ABJ(M) theory to J scalar final states. We work in the ’t Hooft limit and show that the leading quantum correction is \( \mathcal{O}\left( {{\lambda^2}} \right) \), where λ is the ’t Hooft coupling. We evaluate this leading correction using standard Feynman diagrams and dimensional regularization, and find that the leading divergence is 1/ϵ2 where the spacetime dimension is d = 3 − 2ϵ. We further find that the result respects maximal transcendentality.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [hep-th/0505205] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 828 (2010) 317 [arXiv:0807.1095] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N =4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. P. Caputa and B.A.E. Mohammed, From Schurs to giants in ABJ(M), JHEP 01 (2013) 055 [arXiv:1210.7705] [INSPIRE].

    Article  ADS  Google Scholar 

  8. S. Hirano, C. Kristjansen and D. Young, Giant gravitons on AdS 4 × CP 3 and their holographic three-point functions, JHEP 07 (2012) 006 [arXiv:1205.1959] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, JHEP 08 (2012) 134 [arXiv:1203.1913] [INSPIRE].

    Article  ADS  Google Scholar 

  10. V. Cardinali, L. Griguolo, G. Martelloni and D. Seminara, New supersymmetric Wilson loops in ABJ(M) theories, Phys. Lett. B 718 (2012) 615 [arXiv:1209.4032] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. O.T. Engelund and R. Roiban, Correlation functions of local composite operators from generalized unitarity, JHEP 03 (2013) 172 [arXiv:1209.0227] [INSPIRE].

    Article  ADS  Google Scholar 

  12. W. van Neerven, Infrared behavior of on-shell form-factors in a N = 4 supersymmetric Yang-Mills field theory, Z. Phys. C 30 (1986) 595 [INSPIRE].

    ADS  Google Scholar 

  13. K. Selivanov, On tree form-factors in (supersymmetric) Yang-Mills theory, Commun. Math. Phys. 208 (2000) 671 [hep-th/9809046] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. A. Brandhuber, B. Spence, G. Travaglini and G. Yang, Form factors in N = 4 super Yang-Mills and periodic Wilson loops, JHEP 01 (2011) 134 [arXiv:1011.1899] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. A. Brandhuber, O. Gurdogan, R. Mooney, G. Travaglini and G. Yang, Harmony of super form factors, JHEP 10 (2011) 046 [arXiv:1107.5067] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. A. Brandhuber, G. Travaglini and G. Yang, Analytic two-loop form factors in N = 4 SYM, JHEP 05 (2012) 082 [arXiv:1201.4170] [INSPIRE].

    Article  ADS  Google Scholar 

  17. L. Bork, D. Kazakov and G. Vartanov, On form factors in N = 4 SYM, JHEP 02 (2011) 063 [arXiv:1011.2440] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. L. Bork, D. Kazakov and G. Vartanov, On MHV form factors in superspace for \( \mathcal{N} \) = 4 SYM theory, JHEP 10 (2011) 133 [arXiv:1107.5551] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. O. Aharony, O. Bergman and D.L. Jafferis, Fractional M 2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. A. Brandhuber, O. Gurdogan, D. Korres, R. Mooney and G. Travaglini, Two-loop Sudakov form factor in ABJM, arXiv:1305.2421 [INSPIRE].

  21. J. Minahan, O. Ohlsson Sax and C. Sieg, Anomalous dimensions at four loops in N = 6 superconformal Chern-Simons theories, Nucl. Phys. B 846 (2011) 542 [arXiv:0912.3460] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  23. A. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].

    Article  ADS  Google Scholar 

  24. T. Gehrmann, T. Huber and D. Maître, Two-loop quark and gluon form-factors in dimensional regularisation, Phys. Lett. B 622 (2005) 295 [hep-ph/0507061] [INSPIRE].

    ADS  Google Scholar 

  25. T. Huber and D. Maˆıtre, HypExp: a Mathematica package for expanding hypergeometric functions around integer-valued parameters, Comput. Phys. Commun. 175 (2006) 122 [hep-ph/0507094] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  26. T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. A. Agarwal, N. Beisert and T. McLoughlin, Scattering in mass-deformed N ≥ 4 Chern-Simons models, JHEP 06 (2009) 045 [arXiv:0812.3367] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. 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].

    Article  ADS  Google Scholar 

  29. T. Bargheer, N. Beisert, F. Loebbert, T. McLoughlin, N. Beisert, et al., Conformal anomaly for amplitudes in \( \mathcal{N} \) = 6 superconformal Chern-Simons theory, J. Phys. A 45 (2012) 475402 [arXiv:1204.4406] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  31. S. Caron-Huot and Y.-t. Huang, The two-loop six-point amplitude in ABJM theory, JHEP 03 (2013) 075 [arXiv:1210.4226] [INSPIRE].

    Article  ADS  Google Scholar 

  32. M.S. Bianchi, G. Giribet, M. Leoni and S. Penati, Light-like Wilson loops in ABJM and maximal transcendentality, arXiv:1304.6085 [INSPIRE].

  33. J.M. Henn, J. Plefka and K. Wiegandt, Light-like polygonal Wilson loops in 3D Chern-Simons and ABJM theory, JHEP 08 (2010) 032 [Erratum ibid. 1111 (2011) 053] [arXiv:1004.0226] [INSPIRE].

  34. M.S. Bianchi et al., From correlators to Wilson loops in Chern-Simons matter theories, JHEP 06 (2011) 118 [arXiv:1103.3675] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. 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].

    Article  MathSciNet  ADS  Google Scholar 

  36. K. Wiegandt, Equivalence of Wilson loops in \( \mathcal{N} \) = 6 super Chern-Simons matter theory and \( \mathcal{N} \) =4 SYM theory, Phys. Rev. D 84 (2011) 126015 [arXiv:1110.1373] [INSPIRE].

    ADS  Google Scholar 

  37. D. Gang, Y.-t. Huang, E. Koh, S. Lee and A.E. Lipstein, Tree-level recursion relation and dual superconformal symmetry of the ABJM theory, JHEP 03 (2011) 116 [arXiv:1012.5032] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. T. Bargheer, F. Loebbert and C. Meneghelli, Symmetries of tree-level scattering amplitudes in N = 6 superconformal Chern-Simons theory, Phys. Rev. D 82 (2010) 045016 [arXiv:1003.6120] [INSPIRE].

    ADS  Google Scholar 

  39. Z. Bern, J. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  40. R.H. Boels, B.A. Kniehl, O.V. Tarasov and G. Yang, Color-kinematic duality for form factors, JHEP 02 (2013) 063 [arXiv:1211.7028] [INSPIRE].

    Article  ADS  Google Scholar 

  41. T. Bargheer, S. He and T. McLoughlin, New relations for three-dimensional supersymmetric scattering amplitudes, Phys. Rev. Lett. 108 (2012) 231601 [arXiv:1203.0562] [INSPIRE].

    Article  ADS  Google Scholar 

  42. L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. W. Chen, G.W. Semenoff and Y.-S. Wu, Two loop analysis of nonAbelian Chern-Simons theory, Phys. Rev. D 46 (1992) 5521 [hep-th/9209005] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NORDITA, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691, Stockholm, Sweden

    Donovan Young

Authors
  1. Donovan Young
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Donovan Young.

Additional information

ArXiv ePrint: 1305.2422

Rights and permissions

Reprints and permissions

About this article

Cite this article

Young, D. Form factors of chiral primary operators at two loops in ABJ(M). J. High Energ. Phys. 2013, 49 (2013). https://doi.org/10.1007/JHEP06(2013)049

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2013)049

Keywords

Search

Navigation