A manifestly MHV Lagrangian for \( \mathcal{N} = 4 \) Yang-Mills. (English) Zbl 1296.81052
Summary: We derive a manifestly MHV Lagrangian for the \( \mathcal{N} = 4 \) supersymmetric Yang-Mills theory in light-cone superspace. This is achieved by constructing a canonical redefinition which maps the \( \mathcal{N} = 4 \) superfield, \(\phi\), and its conjugate, \( \bar{\phi } \), to a new pair of superfields, \(\chi\) and \( \tilde{\chi } \). In terms of these new superfields the \( \mathcal{N} = 4 \) Lagrangian takes a (non-polynomial) manifestly MHV form, containing vertices involving two superfields of negative helicity and an arbitrary number of superfields of positive helicity. We also discuss constraints satisfied by the new superfields, which ensure that they describe the correct degrees of freedom in the \( \mathcal{N} = 4 \) supermultiplet. We test our derivation by showing that an expansion of our superspace Lagrangian in component fields reproduces the correct gluon MHV vertices.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 46S60 | Functional analysis on superspaces (supermanifolds) or graded spaces |
| 70S05 | Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems |
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