D3-branes on the Coulomb branch and instantons

TL;DR

This paper explores the effects of higher derivative interactions in type IIB supergravity on D3-branes, their instanton contributions, and the dual gauge theory, revealing new insights into AdS/CFT correspondence and instanton measures.

Contribution

It analyzes how higher derivative terms affect D3-brane solutions and instanton effects, extending the understanding of the AdS/CFT duality at finite N with constrained instantons.

Findings

Higher derivative interactions do not alter classical D3-brane solutions.

D-instanton contributions appear in effective interactions like C^2 and Lambda^8.

Explicit boundary correlation functions of eight Lambda's are constructed.

Abstract

The relative coefficients of higher derivative interactions of the IIB effective action of the form C^4, (D F_5)^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 \zeroC^2 in this background (where \zero C is the background value of the Weyl tensor) leads to effective O(1/alpha') 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_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 N D3-branes are grouped into r coincident bunches with M_r in each group, with M_r/N = m_r fixed as N goes to infinity. The boundary correlation function of eight Lambda'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.