Instantons in [formula omitted]Sp( N) superconformal gauge theories and the AdS/CFT correspondence

Abstract

We study, using ADHM construction, instanton effects in an N=2 superconformal Sp( N) gauge theory, arising as effective field theory on a system of N D3-branes near an orientifold 7-plane and eight D7-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× 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× S 3, In the second class the geometry is AdS 5× S 5/ Z 2 and on the string theory side it means that the D-instantons are free to move in the ten-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 an odd number of instantons give contributions 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.