Abstract
We compute the supersymmetry constraints on the R^4 type corrections in maximal supergravity in dimension 8, 6, 4 and 3, and determine the tensorial differential equations satisfied by the function of the scalar fields multiplying the R^4 term in the corresponding invariants. The second order derivative of this function restricted to the Joseph ideal vanishes in dimension lower than six. These results are extended to the d^4 R^4 and the d^6 R^4 corrections, based on the harmonic superspace construction of these invariants in the linearised approximation. We discuss the solutions of these differential equations and analysis the consequences on the non-perturbative type II low energy string theory effective action.
Highlights
We compute the supersymmetry constraints on the R4 type corrections in maximal supergravity in dimension 8, 6, 4 and 3, and determine the tensorial differential equations satisfied by the function of the scalar fields multiplying the R4 term in the corresponding invariants
The constraints from supersymmetry have been computed for higher order invariants [14] and the same conclusion holds for the ∇4R4 type corrections [10]
The differential equation that we find to be a consequence of supersymmetry implies strong restrictions on the possible perturbative corrections that the effective action can receive in string theory, and implies through the dependence on the scalar fields that the non-perturbative corrections associated to instantons must be 1/2 BPS by supersymmetry
Summary
In order to determine supersymmetry invariants we shall use the superspace formalism. One straightforwardly checks that they are the only invariant tensors satisfying to the appropriate symmetry properties, and the specific coefficients are determined modulo an overall rescaling by the Bianchi identities (2.14), i.e. indicates the sum over cyclic permutations of the three pairs of indices. In the same way one use the Bianchi identities to show that all the dimension 1/2 component of U(1) weight 1 are determined in terms of a single field λiαjk as. Is invariant with respect to supersymmetry, modulo a total derivative and the classical equations of motion [20, 21] In this form the components L(m,n,p)|θ=0 only depend on the supercovariant field strengths and their supercovariant derivatives. We will find out that these equations alone permit to determine the differential constraints on the function of the scalar fields characterising the d-closed superform
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