Deformations with Maximal Supersymmetries Part 1: On-shell Formulation

TL;DR

This work develops an on-shell, algebraic framework to classify higher-derivative deformations of maximally supersymmetric Yang–Mills theories across dimensions, preserving all $16$ supercharges while allowing Lorentz and/or R-symmetry breaking. Deformations are recast as deformations of the associative algebra generated by super-gauge covariant derivatives, organized via ${ m H}^2(L,U(YM_d))$ and filtered into F-term, D-term, and exceptional D-term sectors through a pure spinor/hypercohomology analysis; the authors provide a comprehensive infinitesimal classification, including Born–Infeld (Lorentz+R-symmetric) and noncommutative (Lorentz-invariant but R-symmetry breaking) cases, plus higher-order obstruction structure. While the on-shell method yields a principled path to all-order deformations, practical obstruction calculations are formidable, and the authors outline a program to address them via non-minimal pure spinor formalism and an off-shell BV framework, with a companion paper dedicated to a Born–Infeld all-orders solution. The results illuminate how maximal SUSY constrains derivative expansions and point to holographic and UV-completion implications, such as the appearance of specific higher-derivative counterterms upon dimensional reduction and potential links to six-dimensional (2,0) theory compactifications and little string theories.

Abstract

We study deformations of maximally supersymmetric gauge theories by higher dimensional operators in various spacetime dimensions. We classify infinitesimal deformations that preserve all 16 supersymmetries, while allowing the possibility of breaking either Lorentz or R-symmetry, using an on-shell algebraic method developed by Movshev and Schwarz. We also consider the problem of extending the deformation beyond the first order.