N=2 Gauge theories on systems of fractional D3/D7 branes

TL;DR

The paper studies four-dimensional N=2 gauge theories with fundamental matter using fractional D3/D7 branes on the Z2 orbifold, addressing naked singularities and the enhançon. It employs boundary-state methods to construct a complete D7 boundary action, solves the full D3/D7 bound-state supergravity solution, and analyzes the dual gauge theory via a probe, showing the perturbative running of the gauge coupling and the emergence of an enhançon scale. A key result is that higher-order twisted terms are necessary for no-force and that the twisted fields contribute only at one loop in the gauge theory, consistent with N=2 non-renormalization. The work extends the gauge/gravity correspondence to N=2 theories with fundamental matter, clarifying the role of twisted moduli and the limits of the supergravity description in the presence of the enhançon.

Abstract

We study a bound state of fractional D3/D7-branes in the ten-dimensional space R^{1,5}*R^{4}/Z_2 using the boundary state formalism. We construct the boundary actions for this system and show that higher order terms in the twisted fields are needed in order to satisfy the zero-force condition. We then find the classical background associated to the bound state and show that the gauge theory living on a probe fractional D3-brane correctly reproduces the perturbative behavior of a four-dimensional N=2 supersymmetric gauge theory with fundamental matter.