D3-branes on the Coulomb branch and instantons

The relative coefficients of higher derivative interactions of the IIB effective action of the form C-4, (DF5)(4), F-5(8),... (where C is the Weyl tensor and F-5 is the five-form field strength) are motivated by supersymmetry arguments. It is shown that the classical supergravity solution for N parallel D3-branes is unaltered by this combination of terms. The non-vanishing of C-0(2) in this background (where C-0 is the background value of the Weyl tensor) leads to effective O(alpha'(-1)) interactions, such as C-2 and Lambda(8) (where Lambda is the dilatino). These contain D-instanton contributions in addition to tree and one-loop terms. The near horizon limit of the N D3-brane system describes a multi-AdS(5) x S-5 geometry that is dual to N = 4 SU(N) Yang-Mills theory spontaneously broken to S(U(M-1) x... x U (M-r)). Here, the D3-branes are grouped into r coincident bunches with M-r in each group, with Sigma(r) M-r = N and M-r/N = m(r) fixed as N --> infinity. The boundary correlation function of eight A's is constructed explicitly. The second part of the paper considers effects of a constrained instanton in this large-N Yang-Mills theory by an extension of the analysis of Dorey, Hollowood and Khoze of the one-instanton measure at finite N. This makes precise the correspondence with the supergravity D-instanton measure at leading order in the 1/N expansion. However, the duality between instanton-induced correlation functions in Yang-Mills theory and the dual supergravity is somewhat obscured by complications relating to the structure of constrained instantons.