We study the dynamics of a N = 2 supersymmetric SU (N ) gauge theory with fundamental or adjoint matter in presence of a non trivial Ω-background along a two dimensional plane. The prepotential and chiral correlators of the gauge theory can be obtained, via a saddle point analysis, from an equation which can be viewed as a non commutative version of the "standard" Seiberg and Witten curve.

Abstract:We discuss unoriented quivers with flavour that arise from D3-branes at local orbifold singularities, in the presence of Ω-planes and non-compact D7-branes. We produce a wide class of unoriented quiver gauge theories, including new instances of N = 1 superconformal theories. We then consider unoriented D-brane instanton corrections of both 'gauge' and 'exotic' kinds. In particular, we show that conformal symmetry can be dynamically broken via the generation of exotic superpotentials. Finally we discuss aspects of the recently proposed N = 1 remnant of N = 4 S-duality. We identify new candidate dual pairs for the C 3 /Z n series of unoriented quiver gauge theories with n odd.

We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a Z 2 orbifold singularity supporting N = 2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is "dual" to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.

We study renormalization group flows among N = 1 SCFTs realized on the worldvolume of D3-branes probing toric Calabi-Yau singularities, thus admitting a brane tiling description. The flows are triggered by masses for adjoint or vector-like pairs of bifundamentals and are generalizations of the Klebanov-Witten construction of the N = 1 theory for the conifold starting from the N = 2 theory for the C 2 /Z 2 orbifold. In order to preserve the toric condition pairs of masses with opposite signs have to be switched on. We offer a geometric interpretation of the flows as complex deformations of the Calabi-Yau singularity preserving the toric condition. For orbifolds, we support this interpretation by an explicit string amplitude computation of the gauge invariant mass terms generated by imaginary self-dual 3-form fluxes in the twisted sector. In agreement with the holographic a-theorem, the volume of the Sasaki-Einstein 5-base of the Calabi-Yau cone always increases along the flow.