A supersymmetric holographic dual of a fractional topological insulator

TL;DR

This paper develops a supersymmetric holographic model of a fractional topological insulator by deriving and solving BPS equations for a probe D7 brane in an AdS background, preserving some supersymmetry.

Contribution

It introduces a supersymmetric extension of a known holographic fractional topological insulator model using D7 branes with nontrivial gauge fields.

Findings

Derived BPS equations from $$-symmetry transformations.

Reduced BPS equations to two nonlinear PDEs.

Numerically obtained solutions representing 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.