A 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 \cite{HoyosBadajoz:2010ac}. This is accomplished by introducing a nontrivial gauge field on the world volume of the probe D7 brane. The BPS equations are derived from the $\kappa$-symmetry transformation of the probe brane. The BPS equations are shown to reduce to two first oder nonlinear partial differential equations. Solutions of the BPS equations correspond to a probe brane configuration which preserves four of the thirty-two supersymmetries of the $AdS_5\times S^5$ background. Solutions of the BPS equations which correspond to a holographic fractional topological insulator are obtained numerically.