Gauge theory amplitudes in twistor space and holomorphic anomaly

By F. Cachazo, Peter Svrček, E. Witten. 2004

161 citations recorded by the source corpus.

We show that, in analyzing differential equations obeyed by one-loop gauge theory amplitudes, one must take into account a certain holomorphic anomaly. When this is done, the results are consistent with the simplest twistor-space picture of the available one-loop amplitudes.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d89977257ab38dbf2789a97b037d366cdf9b20e2

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Citations in the corpus

Non-supersymmetric loop amplitudes and MHV vertices (2004, background): “The question of the localisation of amplitudes was then revisited, and the complications previously found were seen to be due to the appearance of additional inhomogeneous terms [7] in the differential equations obeyed by one-loop amplitudes.”
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].”
Scattering amplitudes, Wilson loops and the string/gauge theory correspondence (2008, background): “At the level of on-shell scattering amplitudes however (super)conformal invariance is obscured beyond tree level; after removing the effects of the (infrared) regulator which explicitly breaks it, the momentum space realization of the generators of the conformal group still exhibits anomalies analog”
One-loop amplitudes of gluons in supersymmetric QCD (2005, unknown): “March 2005”
Cut-constructible part of QCD amplitudes (2006, methodology): “egrals associated to box topologies, without any explicit integration.2 Some related methods are the use of MHV diagrams in the cut calculations [37] and the use [21,38,39] of the holomorphic anomaly [20] to determine certain cut integrals [40,21]. Although supersymmetric multiplets contain more par”
A recursion relation for gravity amplitudes (2005, background): “[12][45][3|4 + 5|6〉〈15〉〈16〉〈12〉〈23〉〈26〉〈34〉〈36〉〈45〉〈46〉〈56〉 +P(2, 3, 4) )”
Unification of residues and Grassmannian dualities (2009, background): “In our previous paper [17], we showed that a natural contour deformation “blows up residues” into a sum over local and non-local terms, making the local spacetime description as manifest as possible by connecting to the light-cone gauge Lagrangian via the CSW/Risager [18, 19, 20, 21, 22] rules.”
Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes (2006, methodology): “First we use Feynman parametrization and then write the integrand as a total derivative [8].”
A direct proof of the CSW rules (2005, background): “It was somewhat unexpected that the rules did apply to loop calculations, but the discrepancy was resolved by the introduction of the ’holomorphic anomaly’ [23].”
MHV rules for Higgs plus multi-gluon amplitudes (2004, background): “This paradox was resolved by the notion of a ‘holomorphic anomaly’ [16] due to singularities in the loop-momentum integration.”
Symmetries of Tree-level Scattering Amplitudes in N = 6 Superconformal Chern{Simons Theory (2010, background): “This is the origin of the holomorphic anomaly [24].”
Scattering amplitudes and Wilson loops in twistor space (2011, background): “An important output of Witten’s twistor-string theory [42] is the MHV formalism, a set of momentum space Feynman rules for calculating scattering amplitudes in N = 4 SYM which are significantly simpler than the ordinary Feynman rules that arise from a spacetime action [79, 82, 83].”