Gauge/Gravity Duals with Holomorphic Dilaton

TL;DR

The paper develops gauge/gravity duals for ${\cal N}=2$ theories with fundamental matter by embedding D7-branes alongside D3-branes and, in a ${\bf Z}_2$ orbifold, fractional D3-branes. It constructs Type B IIB warped backgrounds with holomorphic axio-dilaton $\tau$ and a $(2,1)$ primitive $G_{(3)}$, analyzes D7+D3 and D7+fractional D3 configurations, and computes the moduli-space metric both from supergravity and from the dual gauge theory. A key result is the demonstrated agreement of the moduli-space metric across the dual descriptions in many regimes, together with the identification of UV/IR limitations where the gravity description breaks down due to large curvature, suggesting a lift to IIA in such cases. The work also clarifies the role of probe branes and enhançons in the ${\cal N}=2$ context and discusses how holomorphic dilaton backgrounds modify the duality, with implications for holography in warped, less-supersymmetric geometries.

Abstract

We consider configurations of D7-branes and whole and fractional D3-branes with N=2 supersymmetry. On the supergravity side these have a warp factor, three-form flux and a nonconstant dilaton. We discuss general IIB solutions of this type and then obtain the specific solutions for the D7/D3 system. On the gauge side the D7-branes add matter in the fundamental representation of the D3-brane gauge theory. We find that the gauge and supergravity metrics on moduli space agree. However, in many cases the supergravity curvature is large even when the gauge theory is strongly coupled. In these cases we argue that the useful supergravity dual must be a IIA configuration.