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We consider constraints on higher dimensional operators for supersymmetriceffective field theories. In four dimensions with maximal supersymmetry andSU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F^nwith MHV helicity configurations must satisfy a recursion relation, and arecompletely determined by that of F^4. As the F^4 coefficient is known to beone-loop exact, this allows us to derive exact coefficients for all suchoperators. 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 Coulombbranch effective action, we again find an infinite class of operators whosecoefficient that are determined exactly. We also consider three-dimensional N=8as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, wedemonstrate that the coefficient of dimension-six operator must be proportionalto the square of that of dimension-four.

Exact coefficients for higher dimensional operators with sixteen supersymmetries