Exact coefficients for higher dimensional operators with sixteen supersymmetries

TL;DR

This paper derives exact coefficients for higher dimensional operators in supersymmetric theories with sixteen supercharges, revealing recursive relations and duality consistency across various dimensions.

Contribution

It establishes recursive relations for operator coefficients in maximally supersymmetric theories and provides exact values, extending to multiple dimensions and symmetry breaking scenarios.

Findings

Coefficients of F^n operators are determined by F^4 coefficients.

F^4 coefficient is one-loop exact and fully determines higher operators.

Results are consistent with SL(2,Z) duality symmetry.

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.