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A bstract Four-dimensional $$ \mathcal{N} $$ N = 4 super Yang-Mills, with a codimension-one defect breaking half of the supersymmetry, arises as the field theory description of the D3/D5 intersection in the holographic limit. This is one of the earliest, most extensively studied, and commonly used systems in holography. In this note we give the full R-symmetry-covariant supersymmetry variations for this system. We also provide the supercurrents and compute the algebra of the corresponding supercharges, obtaining the full set of central charges. We show that magnetically charged finite-energy field configurations preserving half of the supersymmetry are solutions to a new form of the extended Bogomolny equations, in which the defect fields play the role of jumping data for the Nahm-like part of the equations. In the appendices, we explain the connection between our results and the superspace-based formulations in the literature. 

Top-down holographic QCD models often work in the “probe” (or “quenched”) limit, which assumes that the number of colors is much greater than the number of flavors. Relaxing this limit is essential to a fuller understanding of holography and more accurate phenomenological predictions. In this work, we focus on a mixing of glueball and meson mass eigenstates that arises from the DBI action as a finite Nf/Nc effect. For concreteness, we work in the Witten-Sakai-Sugimoto model, and show that this mixing must be treated in conjunction with the backreaction of the flavor branes onto the background geometry. Including the backreaction with the simplification that it is “smeared out” over the compact transverse direction, we derive a corrected effective action for the vector glueball and scalar states. Along the way, we observe a Stückelberg-like mechanism that restores translation invariance in the transverse direction. We also derive a general technique, that lends itself easily to numerics, for finding mass eigenstates of Lagrangians with vector-scalar mixing. We then calculate the first order corrections to the mass spectra of both the vector and scalar particles, and show that the term that explicitly mixes vector and scalar states is the most significant correction to the masses of low-lying scalar mesons.