Journal of High Energy Physics

, 2011:77 | Cite as

One-loop amplitudes in six-dimensional (1,1) theories from generalised unitarity

  • Andreas Brandhuber
  • Dimitrios Korres
  • Daniel Koschade
  • Gabriele Travaglini


Recently, the spinor helicity formalism and on-shell superspace were developed for six-dimensional gauge theories with (1,1) supersymmetry. We combine these two techniques with (generalised) unitarity, which is a powerful technique to calculate scattering amplitudes in any massless theory. As an application we calculate one-loop superamplitudes with four and five external particles in the (1,1) theory and perform several consistency checks on our results.


Supersymmetric gauge theory Gauge Symmetry Field Theories in Higher Dimensions 


  1. [1]
    C. Cheung and D. O’Connell, Amplitudes and spinor-helicity in six dimensions, JHEP 07 (2009) 075 [arXiv:0902.0981] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    R. Boels, Covariant representation theory of the Poincaré algebra and some of its extensions, JHEP 01 (2010) 010 [arXiv:0908.0738] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    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
  4. [4]
    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] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    T. Dennen, Y.-t. Huang and W. Siegel, Supertwistor space for 6D maximal super Yang-Mills, JHEP 04 (2010) 127 [arXiv:0910.2688] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    Y.-t. Huang and A.E. Lipstein, Amplitudes of 3D and 6D maximal superconformal theories in supertwistor space, JHEP 10 (2010) 007 [arXiv:1004.4735] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    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
  8. [8]
    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
  9. [9]
    Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One-loop n-point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [SPIRES].ADSCrossRefGoogle Scholar
  11. [11]
    Z. Bern, L.J. Dixon and D.A. Kosower, One-loop amplitudes for e+ e to four partons, Nucl. Phys. B 513 (1998) 3 [hep-ph/9708239] [SPIRES].ADSCrossRefGoogle Scholar
  12. [12]
    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
  13. [13]
    W.L. van Neerven, Dimensional regularization of mass and infrared singularities in two loop on-shell vertex functions, Nucl. Phys. B 268 (1986) 453 [SPIRES].ADSCrossRefGoogle Scholar
  14. [14]
    Z. Bern and A.G. Morgan, Massive loop amplitudes from unitarity, Nucl. Phys. B 467 (1996) 479 [hep-ph/9511336] [SPIRES].ADSCrossRefGoogle Scholar
  15. [15]
    A. Brandhuber, S. McNamara, B.J. Spence and G. Travaglini, Loop amplitudes in pure Yang-Mills from generalised unitarity, JHEP 10 (2005) 011 [hep-th/0506068] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, D-dimensional unitarity cut method, Phys. Lett. B 645 (2007) 213 [hep-ph/0609191] [SPIRES].ADSGoogle Scholar
  17. [17]
    Z. Bern, J.J. Carrasco, T. Dennen, Y.-t. Huang and H. Ita, Generalized unitarity and six-dimensional helicity, arXiv:1010.0494 [SPIRES].
  18. [18]
    P.S. Howe and K.S. Stelle, Ultraviolet divergences in higher dimensional supersymmetric Yang-Mills theories, Phys. Lett. B 137 (1984) 175 [SPIRES].ADSGoogle Scholar
  19. [19]
    Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One-loop self-dual and N = 4 super Yang-Mills, Phys. Lett. B 394 (1997) 105 [hep-th/9611127] [SPIRES].MathSciNetADSGoogle Scholar
  20. [20]
    V.P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett. B 214 (1988) 215 [SPIRES].ADSGoogle Scholar
  21. [21]
    A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473 [SPIRES].
  22. [22]
    Z. Bern, J.J.M. Carrasco, H. Ita, H. Johansson and R. Roiban, On the structure of supersymmetric sums in multi-loop unitarity cuts, Phys. Rev. D 80 (2009) 065029 [arXiv:0903.5348] [SPIRES].MathSciNetADSGoogle Scholar
  23. [23]
    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 [SPIRES].ADSCrossRefGoogle Scholar
  24. [24]
    Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    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] [SPIRES].MathSciNetADSGoogle Scholar
  26. [26]
    B.A. Kniehl and O.V. Tarasov, Analytic result for the one-loop scalar pentagon integral with massless propagators, Nucl. Phys. B 833 (2010) 298 [arXiv:1001.3848] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    M.L. Mangano and S.J. Parke, Multi-parton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [SPIRES].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Andreas Brandhuber
    • 1
  • Dimitrios Korres
    • 1
  • Daniel Koschade
    • 1
  • Gabriele Travaglini
    • 1
  1. 1.Centre for Research in String Theory, Department of Physics, Queen MaryUniversity of LondonLondonUnited Kingdom

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