Abstract

In this talk, I will consider the boundary of time-reversal-invariant topological insulators in three dimensions and I will show that novel quantum phases emerge in presence of geometric deformations and electromagnetic interactions.
In the first part, I will focus on gapped boundary states, where the gap is induced by an external electromagnetic field. By employing a geometric formalism, I will show that these states support a quantum Hall effect, Hall viscosity and thermal Hall effect. The geometric model is an 2+1-dimensional anti-de Sitter (AdS) theory dual to a 1+1-dimensional conformal field theory (CFT), which describes the chiral gapless states trapped along defect lines on the gapped boundary.
In the second part, I will focus on gapless boundary states by showing that quantum electromagnetic interactions induce a novel 2+1-dimensional CFT. This characterizes an interacting gapless phase in analogy to the helical Luttinger liquid proposed in two-dimensional topological insulators. I will discuss its main properties and its connection to a 3+1-dimensional AdS theory