World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory

Details World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory

1998-12-24

arxiv.org/abs/hep-th/9812229v2

Nucl.Phys. B560 (1999) 551-586

Physics

High Energy Physics

High Energy Physics - Theory

37(+1) pages, details added for section 2

Scientific paper

10.1016/S0550-3213(99)00386-7

Based on the world-line formalism with a sewing method, we derive the Yang-Mills effective action in a form useful to generate the Bern-Kosower-type master formulae for gluon scattering amplitudes at the two-loop level. It is shown that four-gluon ($\Phi^4$ type sewing) contributions can be encapsulated in the action with three-gluon ($\Phi^3$ type) vertices only, the total action thus becoming a simple expression. We then derive a general formula for a two-loop Euler-Heisenberg type action in a pseudo-abelian $su(2)$ background. The ghost loop and fermion loop cases are also studied.

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