Exact coefficients for higher dimensional operators with sixteen supersymmetries

Abstract

We consider constraints on higher-dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) Rsymmetry, 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 coefficients 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.

Soft theorems from anomalous symmetries

“…(3.10) with the summation over 1, · · · , n−1. This confirms that in general the soft-limit of the dilaton effective action, is given by 13) in accordance with eq. (3.5).…”

“…Constraints on ∆a in four dimensions were achieved by combining dispersion relations with the optical theorem [7]. In six dimensions, constraints can be found instead by considering supersymmetry [12][13][14]. For completeness, we will derive the six-dimensional SUSY constraints in a much simpler fashion.…”

“…On the other hand, the candidate three-loop counter term, R 4 , has been studied using extended superspace and shown to be consistent with all known symmetries including the U(1) duality symmetry [34]. 13 In this section, we will investigate this issue from on-shell S-matrix point of view, namely we will study whether the S-matrix generated from a single insertion of R 4 , can be completed in a way that is consistent with both N = 4 susy and the soft theorems implied by the duality symmetry. We first note that the operator R 4 cannot generate R-symmetry violating amplitudes, thus the single-soft limits of matrix elements of R 4 should be vanishing for respecting the soft theorems.…”

“…The double-soft-scalar theorems corresponding to duality symmetry for N = 4 supergravity were derived in [13], 24) where anti-symmetrization is introduced to remove the polluted soft-graviton singularity, and the U(1) R-symmetry generator is given by, 25) where Φ and Φ multiplets are defined in eq. (4.1).…”

Effective actions in N = 1 $$ \mathcal{N}=1 $$ , D5 supersymmetric gauge theories: harmonic superspace approach

“…A possible new non-renormalization theorems for Abelian F n was conjectured in [35]. Recently the authors of [36][37][38] systematically analyzed the effective action on the moduli space of (2,0) superconformal field theories in six dimensions, as well as their toroidal compactification to maximally SYM theories in five and four dimensions. They presented an approach to non-renormalization theorems that constrain this effective action.…”