One-loop gauge theory amplitudes in N=4 super Yang-Mills from MHV vertices

By A. Brandhuber, B. Spence, G. Travaglini. 2004

239 citations recorded by the source corpus.

Abstract We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N = 4 super-Yang–Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N = 4 super-Yang–Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of supersymmetric MHV one-loop scattering amplitudes with an arbitrary number of external legs in N = 4 super-Yang–Mills. Remarkably, our approach naturally leads to a representation of the amplitudes as dispersion integrals, which we evaluate exactly. This yields a new, simplified form for the MHV amplitudes, which is equivalent to the expressions obtained previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9e371564f74b3a3fe525926b75b6ae08b4d1512d

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In Nuclear and High Energy Physics

1. Kasper Risager
2. F. Cachazo
3. L. Mason
4. David Skinner
5. V. Khoze
6. A. Brandhuber
7. G. Travaglini
8. R. Britto

Citations in the corpus

• Scattering amplitudes and Wilson loops in twistor space (2011, methodology): “Indeed, it has been shown to compute the correct amplitudes at one-loop explicitly [84], and after being expressed on momentum twistor space (see [21] and section 5 of this review) was shown to be correct to all loop orders for planar N = 4 SYM [37] using an all-line recursion relation building on t”
• Gauge theory amplitudes in twistor space and holomorphic anomaly (2004, background): “We have reconsidered these issues because of a new computation of the one-loop N = 4 MHV amplitudes [ 6 ].”
• Recursion relations for gauge theory amplitudes with massive particles. (2005, methodology): “At one loop, the MHV rules have been successfully applied to supersymmetric amplitudes [25–31].”
• Supersymmetric gauge theories in twistor space (2006, background): “form loops [ 12 ] obtaining expressions that agree with N = 4 1-loop amplitudes in the literature [13].”
• A direct proof of the CSW rules (2005, methodology): “ts in tree-level calculations [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], and it was also used for some one-loop calculations in an approach developed by Brandhuber, Spence and Travaglini [19, 20, 21, 22]. It was somewhat unexpected that the rules did apply to loop calculations, but the ”
• MHV rules for Higgs plus multi-gluon amplitudes (2004, methodology): “Brandhuber, Spence and Travaglini [11] used MHV rules to reproduce the series of one-loop n-gluon MHV amplitudes in N = 4 SYM, previously computed via unitarity cuts [12].”
• A Note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix (2008, methodology): “15) = λ̃3 〈12〉 (〈23〉[23] + 〈31〉[31] + 〈12〉[12]) (2.”
• The Lagrangian origin of MHV rules. (2005, unknown): “The construction extends to include massless fermions.”
• The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space (2010, methodology): “9) agrees identically with the integrand of the momentum twistor form of the n-particle 1-loop MHV amplitude as presented in [1], which was proved to be equivalent to the expression for the 1-loop MHV amplitude obtained from the standard MHV rules in momentum space [24, 51, 52].”