Download PDF

Journal of High Energy Physics

, 2017:24 | Cite as

A note on NMHV form factors from the Graßmannian and the twistor string

  • David Meidinger
  • Dhritiman Nandan
  • Brenda Penante
  • Congkao Wen
Open Access
Regular Article - Theoretical Physics
First Online:
Received:
Accepted:

Abstract

In this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in \( \mathcal{N}=4 \) superconformal Yang-Mills theory. We present an all-n contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation. In addition, we study other G(3, n + 2) formulas obtained from the connected prescription introduced recently. We find a recursive expression for all n and study its properties. For n ≥ 6, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes.

Keywords

Duality in Gauge Field Theories Scattering Amplitudes Supersymmetric Gauge Theory 
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]
    E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    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].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    L. Ferro, T. Lukowski, C. Meneghelli, J. Plefka and M. Staudacher, Spectral parameters for scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 01 (2014) 094 [arXiv:1308.3494] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    D. Chicherin, S. Derkachov and R. Kirschner, Yang-Baxter operators and scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 881 (2014) 467 [arXiv:1309.5748] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A duality for the S matrix, JHEP 03 (2010) 020 [arXiv:0907.5418] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    N. Arkani-Hamed et al., Scattering Amplitudes and the Positive Grassmannian, Cambridge University Press, Cambridge U.K. (2012), arXiv:1212.5605.
  8. [8]
    B. Eden, P. Heslop and L. Mason, The correlahedron, arXiv:1701.00453 [INSPIRE].
  9. [9]
    N. Arkani-Hamed and J. Trnka, The amplituhedron, JHEP 10 (2014) 030 [arXiv:1312.2007] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    N. Arkani-Hamed and J. Trnka, Into the amplituhedron, JHEP 12 (2014) 182 [arXiv:1312.7878] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    A. Brandhuber, O. Gurdogan, R. Mooney, G. Travaglini and G. Yang, Harmony of super form factors, JHEP 10 (2011) 046 [arXiv:1107.5067] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    L.V. Bork, On NMHV form factors in N = 4 SYM theory from generalized unitarity, JHEP 01 (2013) 049 [arXiv:1203.2596] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    L.V. Bork, On form factors in \( \mathcal{N}=4 \) SYM theory and polytopes, JHEP 12 (2014) 111 [arXiv:1407.5568] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    L.V. Bork and A.I. Onishchenko, Grassmannians and form factors with q 2 = 0 in \( \mathcal{N}=4 \) SYM theory, JHEP 12 (2016) 076 [arXiv:1607.00503] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    L.V. Bork and A.I. Onishchenko, Form factors in the \( \mathcal{N}=4 \) maximally supersymmetric Yang-Mills theory, soft theorems, and integrability, Theor. Math. Phys. 190 (2017) 335.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: part I, Nucl. Phys. B 869 (2013) 329 [arXiv:1103.3714] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: part II, Nucl. Phys. B 869 (2013) 378 [arXiv:1103.4353] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    R. Frassek, D. Meidinger, D. Nandan and M. Wilhelm, On-shell diagrams, Graßmannians and integrability for form factors, JHEP 01 (2016) 182 [arXiv:1506.08192] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    J.A. Farrow and A.E. Lipstein, From 4D ambitwistor strings to on shell diagrams and back, JHEP 07 (2017) 114 [arXiv:1705.07087] [INSPIRE].CrossRefGoogle Scholar
  22. [22]
    M. Spradlin and A. Volovich, From twistor string theory to recursion relations, Phys. Rev. D 80 (2009) 085022 [arXiv:0909.0229] [INSPIRE].
  23. [23]
    L. Dolan and P. Goddard, Gluon tree amplitudes in open twistor string theory, JHEP 12 (2009) 032 [arXiv:0909.0499] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory, Phys. Rev. D 70 (2004) 026009 [hep-th/0403190] [INSPIRE].
  25. [25]
    N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-matrix in twistor space, JHEP 03 (2010) 110 [arXiv:0903.2110] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    D. Nandan, A. Volovich and C. Wen, A Grassmannian etude in NMHV minors, JHEP 07 (2010) 061 [arXiv:0912.3705] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  27. [27]
    N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, Unification of residues and Grassmannian dualities, JHEP 01 (2011) 049 [arXiv:0912.4912] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    J.L. Bourjaily, J. Trnka, A. Volovich and C. Wen, The Grassmannian and the twistor string: connecting all trees in N = 4 SYM, JHEP 01 (2011) 038 [arXiv:1006.1899] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    A. Brandhuber, E. Hughes, R. Panerai, B. Spence and G. Travaglini, The connected prescription for form factors in twistor space, JHEP 11 (2016) 143 [arXiv:1608.03277] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    S. He and Z. Liu, A note on connected formula for form factors, JHEP 12 (2016) 006 [arXiv:1608.04306] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    S. Franco, D. Galloni, B. Penante and C. Wen, Non-planar on-shell diagrams, JHEP 06 (2015) 199 [arXiv:1502.02034] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    J.L. Bourjaily, S. Franco, D. Galloni and C. Wen, Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams, JHEP 10 (2016) 003 [arXiv:1607.01781] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    L.V. Bork and A.I. Onishchenko, Four dimensional ambitwistor strings and form factors of local and Wilson line operators, arXiv:1704.04758 [INSPIRE].
  34. [34]
    H.S. White, Seven points on a twisted cubic curve, Proc. Natl. Acad. Sci. 1 (1915) 464.ADSCrossRefMATHGoogle Scholar
  35. [35]
    D. Nandan and C. Wen, Generating all tree amplitudes in N = 4 SYM by inverse soft limit, JHEP 08 (2012) 040 [arXiv:1204.4841] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Institut für Mathematik und Institut für PhysikHumboldt-Universität zu Berlin, and IRIS GebäudeBerlinGermany
  2. 2.Higgs Centre for Theoretical Physics, School of Physics and AstronomyThe University of EdinburghEdinburghU.K.
  3. 3.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  4. 4.CERN Theory DivisionGeneva 23Switzerland
  5. 5.Walter Burke Institute for Theoretical PhysicsCalifornia Institute of TechnologyPasadenaU.S.A.
  6. 6.Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and AstronomyUCLALos AngelesU.S.A.

Personalised recommendations