A quantization of twistor Yang-Mills theory through the background field method

Abstract

Four dimensional Yang-Mills theory formulated through an action on twistor space has a larger gauge symmetry than the usual formulation, which in previous work was shown to allow a simple gauge transformation between text-book perturbation theory and the Cachazo-Svrcek-Witten rules. In this paper we study non-supersymmetric twistor Yang-Mills theory at loop level using the background field method. For an appropriate partial quantum field gauge choice it is shown the calculation of the effective action is equivalent to (the twistor lift of) the calculation in ordinary Yang-Mills theory in the Chalmers and Siegel formulation to all orders in perturbation theory. A direct consequence is that the twistor version of Yang-Mills theory is just as renormalizable in this particular gauge. As applications an explicit calculation of the Yang-Mills beta function and some preliminary investigations into using the formalism to calculate S-matrix elements at loop level are presented. In principle the technique described in this paper generates consistent quantum completions of the CSW rules. However, by inherent limitations of the partial gauge choice employed here, this offers in its current form mainly simplifications for tree level forestry. The method is expected to be applicable to a wide class of four dimensional gauge theories.

29 pages, v2: typos, v3: bibliography error fixed, v4: added references, comment on all plus amplitudes within setup

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Cited by in corpus (15)

• Loop amplitudes in gauge theories: modern analytic approaches
• Gravity, Twistors and the MHV Formalism
• One-loop MHV Rules and Pure Yang-Mills
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• CSW rules for a massive scalar
• Self-Dual Supergravity and Twistor Theory
• Gluon scattering on self-dual radiative gauge fields
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• Yang-Mills Theory in Twistor Space
• The MHV Lagrangian for a spontaneously broken gauge theory
• Infinite Dimensional Symmetries of Self-Dual Yang-Mills
• MHV Lagrangians for Yang--Mills and QCD
• Symmetries of the Self-Dual Sector of N=4 Super Yang-Mills on the Light Cone
• S-matrix equivalence restored
• On perturbative field theory and twistor string theory