Multi-instanton calculus and the AdS/CFT correspondence in = 4 superconformal field theory

Abstract

We present a self-contained study of ADHM multi-instantons in SU(N) gauge theory, especially the novel interplay with supersymmetry and the large-N limit. We give both field-and string-theoretic derivations of the N = 4 supersymmetric multi-instanton action and collective coordinate integration measure. As a central application, we focus on certain n-point functions G n , n = 16, 8 or 4, in N = 4 SU(N) gauge theory at the conformal point (as well as on related higher-partial-wave correlators); these are correlators in which the 16 exact supersymmetric and superconformal fermion zero modes are saturated. In the large-N limit, for the first time in any 4-dimensional theory, we are able to evaluate all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of a single copy of AdS 5 × S 5 . (2) The integration measure on this space includes the partition function of 10-dimensional N = 1 SU(k) gauge theory dimensionally reduced to 0 dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Type IIB string calculations, at the k-instanton level,

Classical gauge instantons from open strings

“…Moreover, from (5.15) one can see that 17) which is indeed the leading term at large distance of the exact instanton solution (see for example appendix B). As before, the subleading terms are given by diagrams with more insertions of source terms.…”

“…The role of D-instantons and their relation to the gauge theory instantons have been intensively studied from many different points of view in the last years (see for example Refs. [10,11,12,14,13,15,16,17,18]; for recent reviews on this subject see Refs. [20,21,22] and references therein).…”

SO and USp Kähler and hyper-Kähler quotients and lumps

“…The moduli space of k instantons in SO(N C ) and USp(2M C ) gauge theories are known to be given by USp(2k) and O(k) hyperKähler quotients, respectively [11,12]. Compared with our spaces in Eqs.…”

“…Of course, to justify this expectation, we need to verify an equivalence 12 between the two formalisms, the moduli matrix formalism and the holomorphic map (4.4) with the constraint on the invariants, under the lump condition. In examples of the next subsection, we just assume that this expectation is true.…”

“…Still we neglect the kinetic terms associated with the vector multiplet, such that the vector multiplet is an auxiliary superfield. The Kähler potential is given by 12) where V e is a U(1) vector supermultiplet and the chiral fields Q have U(1) charge +1. The…”