Instantons in ${\cal N}=2$ $Sp(N)$ Superconformal Gauge Theories and the AdS/CFT Correspondence

TL;DR

This paper investigates instanton effects in ${ m extbf{N}}=2$ $Sp(N)$ superconformal gauge theories using ADHM construction, analyzing their measure, large-N saddle points, and matching correlators with string theory predictions within the AdS/CFT framework.

Contribution

It provides a detailed analysis of instanton measures, identifies two classes of saddle points with distinct geometries, and confirms the AdS/CFT correspondence through correlator comparisons in an ${ m extbf{N}}=2$ $Sp(N)$ setting.

Findings

Two classes of saddle points with $AdS_5\times S^3$ and $AdS_5\times S^5/Z_2$ geometries.

Matching of a four-flavour-current correlator with string theory $F^4$ coupling results.

Observation of O(8) symmetry breaking to SO(8) due to instanton sectors.

Abstract

We study, using ADHM construction, instanton effects in an ${\CN}=2$ superconformal $Sp(N)$ gauge theory, arising as effective field theory on a system of $N$ D-3-branes near an orientifold 7-plane and 8 D-7-branes in type I' string theory. We work out the measure for the collective coordinates of multi-instantons in the gauge theory and compare with the measure for the collective coordinates of $(-1)$-branes in the presence of 3- and 7-branes in type I' theory. We analyse the large-N limit of the measure and find that it admits two classes of saddle points: In the first class the space of collective coordinates has the geometry of $AdS_5\times S^3$ which on the string theory side has the interpretation of the D-instantons being stuck on the 7-branes and therefore the resulting moduli space being $AdS_5\times S^3$, In the second class the geometry is $AdS_5\times S^5/Z_2$ and on the string theory side it means that the D-instantons are free to move in the 10-dimensional bulk. We discuss in detail a correlator of four O(8) flavour currents on the Yang-Mills side, which receives contributions from the first type of saddle points only, and show that it matches with the correlator obtained from $F^4$ coupling on the string theory side, which receives contribution from D-instantons, in perfect accord with the AdS/CFT correspondence. In particular we observe that the sectors with odd number of instantons give contribution to an O(8)-odd invariant coupling, thereby breaking O(8) down to SO(8) in type I' string theory. We finally discuss correlators related to $R^4$, which receive contributions from both saddle points.