Supersymmetric holographic dual of a fractional topological insulator

Abstract

We construct a supersymmetric generalization of the holographic dual of a fractional topological insulator found in [23]. This is accomplished by introducing a nontrivial gauge field on the world volume of the probe $D7$-brane. The Bogomol'nyi-Prasad-Sommerfeld monopoles (BPS) equations are derived from the $\ensuremath{\kappa}$-symmetry transformation of the probe brane. The BPS equations are shown to reduce to two first-order nonlinear partial differential equations. Solutions of the BPS equations correspond to a probe brane configuration which preserves four of the 32 supersymmetries of the $Ad{S}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ background. Solutions of the BPS equations which correspond to a holographic fractional topological insulator are obtained numerically.