Emergent Weyl spinors in multifermion systems
Abstract
In Ref. [1] Hořava suggested, that the multifermion manybody system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarsegrained fermions. The number of the components of these coarsegrained fermions is reduced compared to the original system. Here we consider the 3+1 D system and concentrate on the particular case when the Fermi surface has codimension p=3, i.e. it represents the Fermi point in momentum space. First we demonstrate explicitly that in agreement with Hořava conjecture, in the vicinity of the Fermi point the original system is reduced to the model with twocomponent Weyl spinors. Next, we generalize the construction of Hořava to the situation, when the original 3+1 D theory contains multicomponent Majorana spinors. In this case the system is also reduced to the model of the twocomponent Weyl fermions in the vicinity of the topologically stable Fermi point. Those fermions experience the emergent gauge field and the gravitational field given by the emergent vierbein. Both these fields (the emergent gauge field and the emergent gravitational field) originate from certain collective excitations of the original system. We speculate, that the given construction may be relevant for the high energy physics in the paradigm, in which the Lorentz symmetry as well as the gravitational and gauge fields are the emergent phenomena, i.e. they appear dynamically in the low energy approximation of the underlined high energy theory.
 Publication:

Nuclear Physics B
 Pub Date:
 April 2014
 DOI:
 10.1016/j.nuclphysb.2014.02.018
 arXiv:
 arXiv:1402.5700
 Bibcode:
 2014NuPhB.881..514V
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 to appear in Nuclear Physics B. Nucl.Phys.B (2014). arXiv admin note: substantial text overlap with arXiv:1312.1267