We consider D7-branes in the gauge theory/string theory correspondence, using a probe approximation. The D7-branes have four directions embedded holomorphically in a non-compact Calabi-Yau 3-fold (which for specificity we take to be the conifold) and their remaining four directions are parallel to a stack of D3-branes transverse to the Calabi-Yau space. The dual gauge theory, which has N = 1 supersymmetry, contains quarks which transform in the fundamental representation of the gauge group, and we identify the interactions of these quarks in terms of a superpotential. By activating three-form fluxes in the gravity background, we obtain a dual gauge theory with a cascade of Seiberg dualities. We find a supersymmetric supergravity solution for the leading backreaction effects of the D7-branes, valid for large radius. The cascading theory with flavors exhibits the interesting phenomenon that the rate of the cascade slows and can stop as the theory flows to the infrared.

We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the Y 2,1 quiver gauge theory corresponding to a cone over the first del Pezzo surface, dP 1 . This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solutions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomalyfree fractional branes.

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d = 3 gauge theories, focusing on the examples of the N = 4 supersymmetric U (N ) × U (N + M ) Yang-Mills theory and the N = 3 supersymmetric U (N ) × U (N + M ) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N = 4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N = 3 case, which (for some values of N and M ) flows to an N = 6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B 2 field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N = 3 theories may exhibit, for some values of N and M , duality cascades similar to those of the Klebanov-Strassler theory.1 The minus sign is the result of the conventions used in this paper, summarized in appendix B.

We reconsider the relationship between the bound state and the SU (3) rigid rotator approaches to strangeness in the Skyrme model. For non-exotic S = −1 baryons the bound state approach matches for small m K onto the rigid rotator approach, and the bound state mode turns into the rotator zero-mode. However, for small m K , we find no S = +1 kaon bound states or resonances in the spectrum, confirming previous work. This suggests that, at least for large N and small m K , the exotic state may be an artifact of the rigid rotator approach to the Skyrme model. An S = +1 near-threshold state comes into existence only for sufficiently large SU (3) breaking. If such a state exists, then it has the expected quantum numbers of Θ + : I = 0, J = 1 2 and positive parity. Other exotic states with (I = 1, J P = 3 2 + ), (I = 1, J P = 1 2 + ), (I = 2, J P = 5 2 + ) and (I = 2, J P = 3 2 + ) appear as its SU (2) rotator excitations. As a test of our methods, we also identify a D-wave S = −1 near-threshold resonance that, upon SU (2) collective coordinate quantization, reproduces the mass splittings of the observed states Λ(1520), Σ(1670) and Σ(1775) with good accuracy.

We study effects associated with the chiral anomaly for a cascading SU (N + M ) × SU (N ) gauge theory using gauge/gravity duality. In the gravity dual the anomaly is a classical feature of the supergravity solution, and the breaking of the U (1) R-symmetry down to Z 2M proceeds via the Higgs mechanism.