Exact coefficients for higher dimensional operators with sixteen supersymmetries

TL;DR

This work uses an on-shell, locality-focused amplitude approach to constrain higher-dimensional operators in theories with sixteen supercharges. It shows that in 4D N=4 with SU(4) R-symmetry, the coefficients of abelian MHV operators are recursively fixed by the $F^4$ term, which is one-loop exact, and that similar relations extend to Coulomb-branch Sp(4) invariants as well as to 3D and 6D theories, where the dimension-six coefficient is tied to the square of the dimension-four coefficient. The authors provide explicit one-loop calculations for $F^4$ and $F^4\phi$, demonstrate compatibility with SL(2,$\mathbb{Z}$) duality, and show that in lower/higher dimensions no independent local dimension-six invariants exist. The results yield an exact, infinite-set prediction for higher-derivative terms and suggest a unified pattern across dimensions, with potential non-abelian extensions to be explored.

Abstract

We consider constraints on higher dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F^n with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F^4. As the F^4 coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficient that are determined exactly. We also consider three-dimensional N=8 as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.