D3-branes on the Coulomb branch and instantons

TL;DR

The paper investigates how $O({\alpha^{\prime}}^{-1})$ higher-derivative corrections in the Type IIB action behave in backgrounds of parallel D3-branes and how D-instantons map to Yang–Mills instantons on the boundary. It shows that a supersymmetry-and-modularity–driven ${\cal R}^4$-type structure, with a modular coefficient $f^{(0,0)}(\tau,\bar{\tau})$, organizes the corrections and leaves the classical D3 background unchanged at this order, while generating nonzero ${}^0 C^2$ and ${}^0 \Lambda^8$ terms with D-instanton content. The dilatino bulk-to-boundary propagator and the eight-dilatino amplitude are constructed to illustrate the D-instanton contributions, tying them to the eight fermionic moduli of the instanton. In the non-conformal sector of ${\cal N}=4$ SYM at large $N$, the constrained one-instanton measure extends to multi-centred vacua, and the leading large-$N$ behaviour shows the measure is proportional to $\partial_\chi^2\partial_\chi^2\sqrt H$, matching the harmonic function $H$ that appears in the near-horizon D3-brane geometry. Altogether, the results strengthen the holographic link between D-instanton effects in IIB string theory and YM instantons in deformed ${\cal N}=4$ theories, albeit with caveats arising from constrained instanton structures.

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.