AdS-sliced flavor branes and adding flavor to the Janus solution

Abstract

We implement D7 flavor branes in anti-de Sitter-sliced coordinates on ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ with the ansatz that the brane fluctuates only in the warped ($\ensuremath{\mu}$) direction in this slicing, which is particularly appropriate for studying the Janus solution. The natural field theory dual in this slicing is $\mathcal{N}=4$ super-Yang--Mills on two copies of ${\mathrm{AdS}}_{4}$. Branes extending from $\ensuremath{\mu}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ can end at different locations, giving rise to quarks with a piecewise constant mass on each ${\mathrm{AdS}}_{4}$ half-space, jumping discontinuously between them. A second class of flavor brane solutions exists in this coordinate system, dubbed ``continuous'' flavor branes, which extend across the entire range of $\ensuremath{\mu}$. We propose that the correct dual interpretation of the ``disconnected'' flavor brane in this ansatz is a quark hypermultiplet with constant mass on one of the ${\mathrm{AdS}}_{4}$ half-spaces with totally reflecting boundary conditions at the boundary of ${\mathrm{AdS}}_{4}$; whereas the dual interpretation of a continuous flavor brane has totally transparent boundary conditions. Numerical studies indicate that AdS-sliced D7 flavor branes of both classes exhibit spontaneous chiral symmetry breaking, as a nonzero vacuum expectation value persists for solutions of the equation of motion down to zero mass. Continuous flavor branes in this ansatz exhibit many other surprising behaviors: their masses seem to be capped at a modest value near $m=0.551$ in units of the inverse AdS radius, and there may be a phase transition between continuous branes of different configurations. We also numerically study quark states in Janus. The behavior of the mass and vacuum expectation value is similar in Janus, including the existence of chiral symmetry breaking at zero mass, though qualitative features of the phase diagram change (sometimes significantly) as the Janus parameter ${c}_{0}$ increases.