Advertisement

Amplitudes and MHV Diagrams

  • Mathew Richard BullimoreEmail author
Chapter
First Online:
  • 441 Downloads
Part of the Springer Theses book series (Springer Theses)

Abstract

Scattering amplitudes are fundamental and remarkably rich observables in quantum field theory. Scattering amplitudes in gauge theories are often much simpler than one expects from a typical Feynman diagram expansion.

Keywords

Momentum Twistor Momentum Space Wavefunction Loop Integrand Dual Superconformal Symmetry Tree-level Superamplitudes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

References

  1. 1.
    S.J. Parke, T. Taylor, An amplitude for \(n\) gluon scattering. Phys. Rev. Lett. 56, 2459 (1986)ADSCrossRefGoogle Scholar
  2. 2.
    E. Witten, Perturbative gauge theory as a string theory in twistor space. Commun. Math. Phys. 252, 189–258 (2004, hep-th/0312171)Google Scholar
  3. 3.
    R. Roiban, M. Spradlin, A. Volovich, On the tree level S matrix of Yang-Mills theory. Phys. Rev. D70, 026009 (2004, hep-th/0403190)Google Scholar
  4. 4.
    R. Britto, F. Cachazo, B. Feng, New recursion relations for tree amplitudes of gluons. Nucl. Phys. B715, 499–522 (2005, hep-th/0412308)Google Scholar
  5. 5.
    R. Britto, F. Cachazo, B. Feng, E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory. Phys. Rev. Lett. 94, 181602 (2005, hep-th/0501052)Google Scholar
  6. 6.
    F. Cachazo, P. Svrcek, E. Witten, MHV vertices and tree amplitudes in gauge theory. JHEP 0409, 006 (2004, hep-th/0403047)Google Scholar
  7. 7.
    K. Risager, A direct proof of the CSW rules. JHEP 0512, 003 (2005, hep-th/0508206)Google Scholar
  8. 8.
    Z. Bern, L.J. Dixon, D.C. Dunbar, D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits. Nucl. Phys. B425, 217–260 (1994, hep-ph/9403226)Google Scholar
  9. 9.
    Z. Bern, L.J. Dixon, D.C. Dunbar, D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes. Nucl. Phys. B435, 59–101 (1995, hep-ph/9409265)Google Scholar
  10. 10.
    C. Berger, Z. Bern, L. Dixon, F. Febres Cordero, D. Forde, et al., An automated implementation of on-shell methods for one-loop amplitudes. Phys. Rev. D78, 036003 (2008, arXiv:0803.4180)Google Scholar
  11. 11.
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231–252 (1998, hep-th/9711200)Google Scholar
  12. 12.
    E. Witten, Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253–291 (1998, hep-th/9802150)Google Scholar
  13. 13.
    S. Gubser, I.R. Klebanov, A.M. Polyakov, Gauge theory correlators from noncritical string theory. Phys. Lett. B428, 105–114 (1998, hep-th/9802109)Google Scholar
  14. 14.
    L.J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359Google Scholar
  15. 15.
    L.J. Dixon, Scattering amplitudes: the most perfect microscopic structures in the universe. J. Phys.A A44, 454001 (2011, arXiv:1105.0771) * Temporary entry*Google Scholar
  16. 16.
    Z. Bern, D.A. Kosower, Color decomposition of one loop amplitudes in gauge theories. Nucl. Phys. B362, 389–448 (1991)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, arXiv:0905.1473Google Scholar
  18. 18.
    L.F. Alday, J.M. Maldacena, Gluon scattering amplitudes at strong coupling. JHEP 0706, 064 (2007, arXiv:0705.0303)Google Scholar
  19. 19.
    G. Korchemsky, J. Drummond, E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops. Nucl. Phys. B795, 385–408 (2008, arXiv:0707.0243)Google Scholar
  20. 20.
    J. Drummond, J. Henn, G. Korchemsky, E. Sokatchev, Conformal ward identities for Wilson loops and a test of the duality with gluon amplitudes. Nucl. Phys. B826, 337–364 (2010, arXiv:0712.1223)Google Scholar
  21. 21.
    J. Drummond, J. Henn, V. Smirnov, E. Sokatchev, Magic identities for conformal four-point integrals. JHEP 0701, 064 (2007, hep-th/0607160)Google Scholar
  22. 22.
    Z. Bern, M. Czakon, L.J. Dixon, D.A. Kosower, V.A. Smirnov, The four-Loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory. Phys. Rev. D75, 085010 (2007, hep-th/0610248)Google Scholar
  23. 23.
    J. Drummond, J. Henn, G. Korchemsky, E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory. Nucl. Phys. B828, 317–374 (2010, arXiv:0807.1095)Google Scholar
  24. 24.
    N. Berkovits, J. Maldacena, Fermionic T-Duality, dual superconformal symmetry, and the amplitude/Wilson loop connection. JHEP 0809, 062 (2008, arXiv:0807.3196)Google Scholar
  25. 25.
    N. Beisert, T-Duality, dual conformal symmetry and integrability for strings on AdS(5) x S**5. Fortsch. Phys. 57, 329–337 (2009, arXiv:0903.0609)Google Scholar
  26. 26.
    J.M. Drummond, J.M. Henn, J. Plefka, Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory. JHEP 0905, 046 (2009, arXiv:0902.2987)Google Scholar
  27. 27.
    J. Drummond, L. Ferro, Yangians Grassmannians and T-duality. JHEP 1007, 027 (2010, arXiv:1001.3348)Google Scholar
  28. 28.
    L. Dolan, C.R. Nappi, E. Witten, A relation between approaches to integrability in superconformal Yang-Mills theory. JHEP 0310, 017 (2003, hep-th/0308089)Google Scholar
  29. 29.
    L. Dolan, C.R. Nappi, E. Witten, Yangian symmetry in D = 4 superconformal Yang-Mills theory, hep-th/0401243Google Scholar
  30. 30.
    N. Arkani-Hamed, F. Cachazo, C. Cheung, J. Kaplan, A duality for the S matrix. JHEP 1003, 020 (2010, arXiv:0907.5418)Google Scholar
  31. 31.
    N. Arkani-Hamed, F. Cachazo, C. Cheung, The Grassmannian origin of dual superconformal invariance. JHEP 1003, 036. (2010, arXiv:0909.0483)Google Scholar
  32. 32.
    L. Mason, D. Skinner, Dual superconformal invariance, momentum twistors and Grassmannians. JHEP 0911, 045 (2009, arXiv:0909.0250)Google Scholar
  33. 33.
    N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot, J. Trnka, The all-loop integrand for scattering amplitudes in planar N=4 SYM. JHEP 1101, 041 (2011, arXiv:1008.2958)Google Scholar
  34. 34.
    J.M. Drummond, J.M. Henn, Simple loop integrals and amplitudes in N=4 SYM. JHEP 1105, 105 (2011, arXiv:1008.2965)Google Scholar
  35. 35.
    J. Drummond, L. Ferro, The Yangian origin of the Grassmannian integral. JHEP 1012, 010 (2010, arXiv:1002.4622)Google Scholar
  36. 36.
    M. Bullimore, D. Skinner, Descent equations for superamplitudes, arXiv:1112.1056Google Scholar
  37. 37.
    S. Caron-Huot, S. He, Jumpstarting the all-loop S-Matrix of planar N=4 super Yang-Mills. JHEP 1207, 174 (2012, arXiv:1112.1060)Google Scholar
  38. 38.
    J. Drummond, J. Henn, G. Korchemsky, E. Sokatchev, Generalized unitarity for N=4 super-amplitudes, arXiv:0808.0491Google Scholar
  39. 39.
    J. Drummond, J. Henn, All tree-level amplitudes in N=4 SYM. JHEP 0904, 018 (2009, arXiv:0808.2475)Google Scholar
  40. 40.
    L. Mason, D. Skinner, Scattering amplitudes and BCFW recursion in twistor space. JHEP 1001, 064 (2010, arXiv:0903.2083)Google Scholar
  41. 41.
    L. Mason, D. Skinner, The complete planar S-matrix of N=4 SYM as a Wilson loop in twistor space. JHEP 1012, 018 (2010, arXiv:1009.2225)Google Scholar
  42. 42.
    L.F. Alday, J.M. Henn, J. Plefka, T. Schuster, Scattering into the fifth dimension of N=4 super Yang-Mills. JHEP 1001, 077 (2010, arXiv:0908.0684)Google Scholar
  43. 43.
    G. Georgiou, V.V. Khoze, Tree amplitudes in gauge theory as scalar MHV diagrams. JHEP 0405, 070 (2004, hep-th/0404072)Google Scholar
  44. 44.
    G. Georgiou, E. Glover, V.V. Khoze, Non-MHV tree amplitudes in gauge theory. JHEP 0407, 048 (2004, hep-th/0407027)Google Scholar
  45. 45.
    R. Boels, C. Schwinn, CSW rules for a massive scalar. Phys. Lett. B662, 80–86 (2008, arXiv:0712.3409)Google Scholar
  46. 46.
    R. Boels, C. Schwinn, CSW rules for massive matter legs and glue loops. Nucl. Phys. Proc. Suppl. 183, 137–142 (2008, arXiv:0805.4577)Google Scholar
  47. 47.
    A. Brandhuber, B.J. Spence, G. Travaglini, One-loop gauge theory amplitudes in N=4 super Yang-Mills from MHV vertices. Nucl. Phys. B706, 150–180 (2005, hep-th/0407214)Google Scholar
  48. 48.
    J. Bedford, A. Brandhuber, B.J. Spence, G. Travaglini, A twistor approach to one-loop amplitudes in N=1 supersymmetric Yang-Mills theory. Nucl. Phys. B706, 100–126 (2005, hep-th/0410280)Google Scholar
  49. 49.
    C. Quigley, M. Rozali, One-loop MHV amplitudes in supersymmetric gauge theories. JHEP 0501, 053 (2005, hep-th/0410278)Google Scholar
  50. 50.
    P. Mansfield, The lagrangian origin of MHV rules. JHEP 0603, 037 (2006, hep-th/0511264)Google Scholar
  51. 51.
    J.H. Ettle, T.R. Morris, Structure of the MHV-rules Lagrangian. JHEP 0608, 003 (2006, hep-th/0605121). Makes major improvements on withdrawn paper hep-th/0605024Google Scholar
  52. 52.
    R. Boels, L. Mason, D. Skinner, From twistor actions to MHV diagrams. Phys. Lett. B648, 90–96 (2007, hep-th/0702035)Google Scholar
  53. 53.
    M. Bullimore, L. Mason, D. Skinner, MHV diagrams in momentum twistor space. JHEP 1012, 032 (2010, arXiv:1009.1854)Google Scholar
  54. 54.
    M. Bullimore, MHV diagrams from an all-line recursion relation, arXiv:1010.5921Google Scholar
  55. 55.
    A. Brandhuber, G. Travaglini, Quantum MHV diagrams, hep-th/0609011Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Mathematical InstituteRadcliffe Observatory QuarterOxfordUK

Personalised recommendations

Cite chapter

Buy options