Summing the Instanton Series in N=2 Superconformal Large-N QCD

TL;DR

This paper computes and sums the multi-instanton measure in large-N N=2 superconformal QCD, revealing a connection to six-dimensional SYM and string theory D-instantons, hinting at an AdS/CFT duality.

Contribution

It provides a closed-form summation of the multi-instanton measure in large-N N=2 superconformal QCD, linking it to six-dimensional SYM and string theory D-instantons.

Findings

Multi-instanton measure collapses to a single AdS_5*S^1 in large-N limit.

The summed measure matches D-instanton normalization in type IIB string theory.

Results suggest a concrete realization of AdS/CFT correspondence.

Abstract

We consider the multi-instanton collective coordinate integration measure in N=2 supersymmetric SU(N) gauge theory with N_F fundamental hypermultiplets. In the large-N limit, at the superconformal point where N_F=2N and all VEVs are turned off, the k-instanton moduli space collapses to a single copy of AdS_5*S^1. The resulting k-instanton effective measure is proportional to N^{1/2} g^4 Z_k^(6), where Z_k^(6) is the partition function of N=(1,0) SYM theory in six dimensions reduced to zero dimensions. The multi-instanton can in fact be summed in closed form. As a hint of an AdS/CFT duality, with the usual relation between the gauge theory and string theory parameters, this precisely matches the normalization of the charge-k D-instanton measure in type IIB string theory compactified to six dimensions on K3 with a vanishing two-cycle.