Instantons in $\mathcal{N}=2$ $Sp(N)$ 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 $Ad{S}_5\times S^3$ 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 $Ad{S}_5\times S^3$, In the second class the geometry is $Ad{S}_5\times S^5/Z_2$ 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.

28 pages, no figures, typos corrected, a reference added

References in corpus (2)

• ADHM and D-instantons in orbifold AdS/CFT duality
• Heterotic/type I duality, D-instantons and an N=2 AdS/CFT correspondence

Cited by in corpus (20)

• TASI Lectures on Solitons
• Multi instanton calculus on ALE spaces
• Heterotic/Type II Triality and Instantons on $K_3$
• Exotic instanton counting and heterotic/type I' duality
• Lectures on instantons
• Yang-Mills- and D-instantons
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• Exotic prepotentials from D(-1)D7 dynamics
• Holography and the Higgs branch of N=2 SYM theories
• Stringy instanton corrections to N=2 gauge couplings
• Classical solutions for exotic instantons?
• Instantons and Emergent AdS_3 x S^3 Geometry
• Instantons, the Information Metric, and the AdS/CFT Correspondence
• Discrete symmetries in the Kaluza-Klein-like theories
• Instantons, finite N=2 Sp(N) theories and the AdS/CFT correspondence
• D1/D5 systems in $\mathcal{N}=4$ string theories
• Non-perturbative effects in the BMN limit of N=4 supersymmetric Yang-Mills
• Twistor Strings with Flavour
• Group-Theoretical Classification of BPS and Possibly Protected States in D=4 Conformal Supersymmetry
• D-instantons and Dualities in String Theory