Holographic flavor on the Higgs branch

In this paper we study the holographic dual, in several spacetime dimensions, of the Higgs branch of gauge theories with fundamental matter. These theories contain defects of various codimensionalities, where the matter fields are located. In the holographic description the matter is added by considering flavor brane probes in the supergravity backgrounds generated by color branes, while the Higgs branch is obtained when the color and flavor branes recombine with each other. We show that, generically, the holographic dual of the Higgs phase is realized by means of the addition of extra flux on the flavor branes and by choosing their appropriate embedding in the background geometry. This suggests a dielectric interpretation in terms of the color branes, whose vacuum solutions precisely match the F- and D-flatness conditions obtained on the field theory side. We further compute the meson mass spectra in several cases and show that when the defect added has codimension greater than zero it becomes continuous and gapless.