Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory

TL;DR

This paper explores integrable deformations of scattering amplitudes in N=4 super Yang-Mills and ABJM theories, introducing deformed Grassmannian integrals and Yangian invariants to deepen understanding of their symmetries.

Contribution

It provides the first explicit construction of deformed Grassmannian integrals and Yangian invariants for both 4d N=4 SYM and 3d ABJM theories, extending the framework of integrability.

Findings

Derived deformed Grassmannian integral for N=4 SYM in momentum and momentum-twistor space.

Initiated the study of deformed scattering amplitudes in ABJM theory.

Constructed algebraic R-matrix for deformed Yangian invariants in ABJM theory.

Abstract

We study Yangian-invariant deformations of scattering amplitudes in 4d N=4 supersymmetric Yang-Mills theory and 3d N=6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Grassmannian integral for 4d N=4 super Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Grassmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.