D3-branes on the Coulomb branch and instantons

The relative coefficients of higher derivative interactions of the IIBeffective action of the form C^4, (D F_5)^4, F_5^8, ... (where C is the Weyltensor and F_5 is the five-form field strength) are motivated by supersymmetryarguments. It is shown that the classical supergravity solution for N parallelD3-branes is unaltered by this combination of terms. The non-vanishing of\zeroC^2 in this background (where \zero C is the background value of the Weyltensor) leads to effective O(1/alpha') interactions, such as C^2 and Lambda^8(where Lambda is the dilatino). These contain D-instanton contributions inaddition to tree and one-loop terms. The near horizon limit of the N D3-branesystem describes a multi-AdS_5xS^5 geometry that is dual to \calN=4 SU(N)Yang-Mills theory spontaneously broken to S(U(M_1)x...xU(M_r)). Here, the ND3-branes are grouped into r coincident bunches with M_r in each group, withM_r/N = m_r fixed as N goes to infinity. The boundary correlation function ofeight Lambda's is constructed explicitly. The second part of the paperconsiders effects of a constrained instanton in this large-N Yang-Mills theoryby an extension of the analysis of Dorey, Hollowood and Khoze of theone-instanton measure at finite N. This makes precise the correspondence withthe supergravity D-instanton measure at leading order in the 1/N expansion.However, the duality between instanton-induced correlation functions inYang-Mills theory and the dual supergravity is somewhat obscured bycomplications relating to the structure of constrained instantons.Comment: 30 pages, JHEP style. Typos corrected and minor clarifications adde