Combined Lorentz symmetry: lessons from superfluid 3He

TL;DR

This paper explores how superfluid helium-3 can model the emergence of combined Lorentz, P, and T symmetries from more fundamental symmetry breaking, with implications for quantum vacuum structure and gravity.

Contribution

It proposes superfluid helium-3 as a condensed matter analog for the origin of combined Lorentz symmetry and explores the resulting topological and gravitational implications.

Findings

Superfluid helium-3 phases model symmetry breaking of the quantum vacuum.

Degeneracy of Minkowski vacuum leads to topological objects like torsion strings.

Multiple tetrads for fermions suggest gravity with several metrics and possible parity violation effects.

Abstract

We consider the possibility of the scenario in which the $P$, $T$ and Lorentz symmetry of the relativistic quantum vacuum are all the combined symmetries. These symmetries emerge as a result of the symmetry breaking of the more fundamental $P$, $T$ and Lorentz symmetries of the original vacuum, which is invariant under separate groups of the coordinate transformations and spin rotations. The condensed matter vacua (ground states) suggest two possible scenarios of the origin of the combined Lorentz symmetry, both are realized in the superfluid phases of liquid $^3$He: the $^3$He-A scenario and the $^3$He-B scenario. In these scenarios the gravitational tetrads are considered as the order parameter of the symmetry breaking in the quantum vacuum. The $^3$He-B scenarios applied to the Minkowski vacuum leads to the continuous degeneracy of the Minkowski vacuum with respect to the $O(3,1)$ spin rotations. The symmetry breaking leads to the corresponding topological objects, which appear due to the nontrivial topology of the manifold of the degenerate Minkowski vacua, such as torsion strings. The 4-fold degeneracy of the Minkowski vacuum with respect to discrete $P$ and $T$ symmetries suggests that the Weyl fermions are described by four different tetrad fields: the tetrad for the left-handed fermions, the tetrad for the right-handed fermions, and the tetrads for their antiparticles. This may lead to the gravity with several metric fields, so that the parity violation may lead to the breaking of equivalence principle. Finally we considered the application of the gravitational tetrads for the solution of the cosmological constant problem.