N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory

Abstract

We present a formulation of the maximally supersymmetric 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 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 N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the 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 N=4 stress-tensor supermultiplet.

51 pages, 4 figures; v2: Appendix B on the propagators in momentum space added. A more detailed comparison with the twistor approach given in Appendix C

References in corpus (2)

• From Twistor Actions to MHV Diagrams
• Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace

Cited by in corpus (13)

• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
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• Conformal anomaly of generalized form factors and finite loop integrals
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• Composite operators and form factors in N=4 SYM
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• N=4 super-Yang-Mills in LHC superspace. Part II: Non-chiral correlation functions of the stress-tensor multiplet
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
• An off-shell superspace reformulation of D=4, N=4 super-Yang-Mills theory
• Twistor fishnets
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Ambitwistor strings and reggeon amplitudes in N=4 SYM