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