Magnetoelectric effect induced by electron-electron interaction in three dimensional topological insulators

We compute the magnetoelectric response of an interacting topological insulator in three space dimensions with a short range interaction between electrons in different orbitals. We show that in the presence of interactions and inverted bands the chiral phase is gauged away and replaced by a topological angle (θ-term) which is determined by saddle point of the interacting action and the Fujikawa integration measure. The magnetoelectric response breaks time reversal symmetry which is restored at strong interactions. The effect is equivalent to the one in four dimensions without interaction; it can be observed by measuring the Faraday rotation under external stress.