One-Loop Effective Action Approach to Quantum MHV Theory

TL;DR

This paper introduces a one-loop effective action method for quantum MHV theory, enabling systematic calculation of loop contributions and addressing limitations of the standard MHV action in loop computations.

Contribution

It formulates the quantum MHV action via a one-loop effective action approach, explicitly integrating quadratic fluctuations and validating with specific amplitude calculations.

Findings

Successfully computes one-loop amplitudes not accessible by standard MHV action

Provides a systematic framework for loop corrections in Yang-Mills related theories

Demonstrates unambiguous definition of loop corrections through field transformations

Abstract

It is well known that the MHV action, i.e. the action containing all the maximally helicity violating vertices, is alone not sufficient for loop computations. In order to develop loop contributions systematically and to ensure that there are no missing terms, we propose to formulate the quantum MHV action via one-loop effective action approach. The quadratic field fluctuations in the light cone Yang-Mills theory are explicitly integrated, followed by the classical canonical field transformation. We test the approach by calculating one loop $(++++)$ and $(+++-)$ amplitudes, i.e. amplitudes that cannot be calculated from ordinary MHV action. Such an approach can be further used to unambiguously define loop corrections in other theories related to Yang-Mills theory by field transformations.