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

TL;DR

This paper demonstrates that twistor space formulation of non-supersymmetric Yang-Mills theory can be quantized using the background field method, maintaining renormalizability and enabling calculations of the beta function and loop-level S-matrix elements.

Contribution

It introduces a background field quantization approach for twistor Yang-Mills theory, showing equivalence to ordinary Yang-Mills calculations and preserving renormalizability in a specific gauge.

Findings

Twistor Yang-Mills theory is renormalizable in the chosen gauge.

The beta function calculation matches that of standard Yang-Mills.

Preliminary loop-level S-matrix computations are feasible with the formalism.

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.