Momentum space topology of fermion zero modes on brane

TL;DR

This paper explores how fermion zero modes on a 3+1 dimensional domain wall in 4+1 spacetime can emerge from nontrivial momentum-space topology, potentially modeling Standard Model particles and gravity without assuming relativistic invariance.

Contribution

It demonstrates that nontrivial bulk fermion topology in 4+1 dimensions leads to chiral fermions and gauge/gravity fields on a 3+1 brane without relying on relativistic symmetry.

Findings

Fermion zero modes arise from bulk topology.

Gauge and gravitational fields emerge from collective modes.

The framework can encompass Standard Model features.

Abstract

We discuss fermion zero modes within the 3+1 brain -- the domain wall between the two vacua in 4+1 spacetime. We do not assume relativistic invariance in 4+1 spacetime, or any special form of the 4+1 action. The only input is that the fermions in bulk are fully gapped and are described by nontrivial momentum-space topology. Then the 3+1 wall between such vacua contains chiral 3+1 fermions. The bosonic collective modes in the wall form the gauge and gravitational fields. In principle, this universality class of fermionic vacua can contain all the ingredients of the Standard Model and gravity.