Abstract

We present a formulation of the maximally supersymmetric mathcal{N} = 4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of mathcal{N} =4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the mathcal{N} = 4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the mathcal{N} = 2 gauge and hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the mathcal{N} = 4 stress-tensor supermultiplet.

Highlights

  • A very old problem in supersymmetric field theory is how to formulate the maximally supersymmetric N = 4 super-Yang-Mills (SYM) theory off shell with full manifest supersymmetry

  • We present a formulation of the maximally supersymmetric N = 4 gauge theory in Lorentz harmonic chiral (LHC) superspace

  • We show that the LHC formulation of the N = 4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N = 2 gauge and hypermultiplet matter theories

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Summary

Introduction

We present a formulation of N = 4 SYM in Lorentz harmonic chiral (LHC) superspace. In it the chiral half of supersymmetry is manifest and realized off shell. The correlators of the N = 4 stresstensor multiplet do not depend on the LHs (they are integrated out) To put it differently, at the end of the calculation we are able to eliminate the infinite sets of auxiliary and pure gauge fields. We use these results in the twin paper [1] for constructing the full (non-chiral) supermultiplet of the N = 4 stress-energy tensor. Appendix B gives a dictionary between the twistor and harmonic languages, for the sake of the reader with a twistor background

Euclidean Lorentz harmonic chiral superspace
Dynamical superfields as gauge super-connections
Reality properties
Coupling constant
Component field content
Yang-Mills theory in Lorentz harmonic space
Supersymmetry of the Chern-Simons action
Full action and modified Qsupersymmetry transformation
Closure of the supersymmetry algebra
Closure of the Qsubalgebra off and on shell
Qsupersymmetry and gauge transformations
Qsupersymmetry in the WZ gauge
Quantization
Light-cone gauge
Green’s functions
Feynman rules
Full propagators
Interpretation as eight-dimensional SYM
Conclusions
Harmonic coset and invariant integral
Harmonic distributions
B Propagators in momentum space
C Relationship with the supertwistor approach
Full Text
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