Abstract
We construct the gravity duals of the Higgs branches of three-dimensional (four-dimensional) super Yang-Mills theories coupled to $N_\textrm{f}$ quark flavors. The effect of the quarks on the color degrees of freedom is included, and corresponds on the gravity side to the backreaction of $N_\textrm{f}$ flavor D6-branes (D7-branes) on the background of $N_\textrm{c}$ color D2-branes (D3-branes). The Higgsing of the gauge group arises from the dissolution of some color branes inside the flavor branes. The dissolved color branes are represented by non-Abelian instantons whose backreaction is also included. The result is a cascading-like solution in which the effective number of color branes varies along the holographic direction. In the three-dimensional case the solution may include an arbitrary number of quasi-conformal (walking) regions.
Highlights
Nf ‘flavor’ D(p+4)-branes [2]
In the so-called alternative quantization, the dual operators have dimension 1, as one would expect at weak coupling for an squark-bilinear operator, and the flow is triggered by a vacuum expectation value (VEV), as one would expect for a state on the Higgs branch
The most dramatic effect of the Higgsing on the gauge theory side is that the effective number of colors decreases with the energy scale from Nc in the UV to nc < Nc in the IR
Summary
We see from the equation of motion for F4 that tr (F ∧ F ) acts as a source for this field, consistent with the fact that an instanton density on the D6-branes corresponds to D2brane charge dissolved on the D6-branes This term encodes the Higgsing of the gauge group and it will allow for its effective rank, as measured by the flux of F4, to run with the holographic coordinate. For the Minkowski components we find: Tμinνst This completes the set of equations to be solved for (A)SD configurations of the gauge field on the flavor branes. The functions h and χ depend only on the radial coordinate r and were determined in [8] by solving two first-order BPS equations In terms of these functions the calibration form that enters the DBI action takes the form. Selfduality is a metric-dependent property, so the particular equations governing it are specific to each of the NK manifolds that we will consider in the subsections
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