Advertisement

From lightcone actions to maximally supersymmetric amplitudes

  • Johannes Broedel
  • Renata Kallosh
Article

Abstract

In this article actions for \( \mathcal{N} = 4 \) SYM and \( \mathcal{N} = 8 \) supergravity are formulated in terms of a chiral superfield, which contains only the physical degrees of freedom of either theory. In these new actions, which originate from the lightcone superspace, the super-gravity cubic vertex is the square of the gauge theory one (omitting the color structures). Amplitude calculations using the corresponding Feynman supergraph rules are tedious, but can be simplified by choosing a preferred superframe. Recursive calculations of all MHV amplitudes in \( \mathcal{N} = 4 \) SYM and the four-point \( \mathcal{N} = 8 \) supergravity amplitude are shown to agree with the known results and connections to the BCFW recursion relations are pointed out. Finally, the new actions are discussed in the context of the double-copy property relating \( \mathcal{N} = 4 \) SYM theory to \( \mathcal{N} = 8 \) supergravity.

Keywords

Extended Supersymmetry Supergravity Models 

Further Reading

  1. [1]
    Z. Bern et al., Three-Loop Superfiniteness of N =8 Supergravity, Phys. Rev. Lett. 98 (2007) 161303 [hep-th/0702112] [SPIRES].ADSCrossRefGoogle Scholar
  2. [2]
    Z. Bern, J.J.Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The Ultraviolet Behavior of N =8 Supergravity at Four Loops, Phys. Rev. Lett. 103 (2009) 081301 [arXiv:0905.2326] [SPIRES].ADSCrossRefGoogle Scholar
  3. [3]
    Z. Bern, J.J.M. Carrasco, H. Johansson and D.A. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops, Phys. Rev. D 76 (2007) 125020 [arXiv:0705.1864] [SPIRES].MathSciNetADSGoogle Scholar
  4. [4]
    J.M. Drummond, J.Henn, G.P. 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] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Generalized unitarity for N =4 super-amplitudes, arXiv:0808.0491 [SPIRES].
  6. [6]
    N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The All-Loop Integrand For Scattering Amplitudes in Planar N =4 SYM, JHEP 01 (2011) 041 [arXiv:1008.2958] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    L. Brink, O. Lindgren and B.E.W. Nilsson, N =4 Yang-Mills Theory on the Light Cone, Nucl. Phys. B 212 (1983) 401 [SPIRES].ADSCrossRefGoogle Scholar
  8. [8]
    S. Mandelstam, Light Cone Superspace and the Ultraviolet Finiteness of the N =4 Model, Nucl. Phys. B 213 (1983) 149 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic Interaction Terms For Arbitrarily Extended Supermultiplets, Nucl. Phys. B 227 (1983) 41 [SPIRES].ADSCrossRefGoogle Scholar
  10. [10]
    S. Ananth, L. Brink and P. Ramond, Eleven-dimensional supergravity in light-cone superspace, JHEP 05 (2005) 003 [hep-th/0501079] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    L. Brink, S.-S. Kim and P. Ramond, E 7(7) on the Light Cone, JHEP 06 (2008) 034 [arXiv:0801.2993] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    A.V. Belitsky, S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Dilatation operator in (super-)Yang-Mills theories on the light-cone, Nucl. Phys. B 708 (2005) 115 [hep-th/0409120] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    R. Kallosh, N =8 Supergravity on the Light Cone, Phys. Rev. D 80 (2009) 105022 [arXiv:0903.4630] [SPIRES].MathSciNetADSGoogle Scholar
  14. [14]
    C.-H. Fu and R. Kallosh, New N =4 SYM Path Integral, Phys. Rev. D 82 (2010) 125022 [arXiv:1005.4171] [SPIRES].ADSGoogle Scholar
  15. [15]
    R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N =4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    A. Brandhuber, P. Heslop and G. Travaglini, A note on dual superconformal symmetry of the N =4 super Yang-Mills S-matrix, Phys. Rev. D 78 (2008) 125005 [arXiv:0807.4097] [SPIRES].MathSciNetADSGoogle Scholar
  18. [18]
    J.M. Drummond and J.M. Henn, All tree-level amplitudes in N =4 SYM, JHEP 04 (2009) 018 [arXiv:0808.2475] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    G. Chalmers and W. Siegel, Simplifying algebra in Feynman graphs. II: Spinor helicity from the spacecone, Phys. Rev. D 59 (1999) 045013 [hep-ph/9801220] [SPIRES].MathSciNetADSGoogle Scholar
  20. [20]
    R. Britto, F. Cachazo and B. Feng, New Recursion Relations for Tree Amplitudes of Gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    R. Britto, F. Cachazo, B. Feng and E. Witten, Direct Proof Of Tree-Level Recursion Relation In Yang-ills Theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    L.J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359 [SPIRES].
  23. [23]
    N. Arkani-Hamed and J. Kaplan, On Tree Amplitudes in Gauge Theory and Gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [SPIRES].MathSciNetCrossRefGoogle Scholar
  24. [24]
    H. Elvang and D.Z. Freedman, Note on graviton MHV amplitudes, JHEP 05 (2008) 096 [arXiv:0710.1270] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    M. Bianchi, H. Elvang and D.Z. Freedman, Generating Tree Amplitudes in N =4 SYM and N =8 SG, JHEP 09 (2008) 063 [arXiv:0805.0757] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    J.M. Drummond, M. Spradlin, A. Volovich and C. Wen, Tree-Level Amplitudes in N =8 Supergravity, Phys. Rev. D 79 (2009) 105018 [arXiv:0901.2363] [SPIRES].MathSciNetADSGoogle Scholar
  27. [27]
    Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [SPIRES].MathSciNetADSGoogle Scholar
  28. [28]
    Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    Z. Bern, J.J.M. Carrasco and H. Johansson, The Structure of Multiloop Amplitudes in Gauge and Gravity Theories, Nucl. Phys. Proc. Suppl. 205 206 (2010) 54 [arXiv:1007.4297] [SPIRES].MathSciNetCrossRefGoogle Scholar
  30. [30]
    Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [SPIRES].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Department of PhysicsStanford UniversityStanfordU.S.A.

Personalised recommendations