Very Special Relativity in Curved Space-Times
Wolfgang Mueck
TL;DR
This paper extends the concept of Very Special Relativity to curved space-times, showing how SIM(2) symmetry can be locally implemented and describing chiral fermions in specific geometries.
Contribution
It generalizes Very Special Relativity to curved backgrounds and constructs locally SIM(2) invariant Lagrangians for chiral fermions.
Findings
Locally SIM(2) invariant Lagrangians can be constructed in curved space-times.
In space-times with SIM(2) holonomy, chiral fermions propagate as massive particles.
Gauging SIM(2) symmetry does not generally couple to gravity.
Abstract
The generalization of Cohen and Glashow's Very Special Relativity to curved space-times is considered. Gauging the SIM(2) symmetry does not, in general, provide the coupling to the gravitational background. However, locally SIM(2) invariant Lagrangians can always be constructed. For space-times with SIM(2) holonomy, they describe chiral fermions propagating freely as massive particles.
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