49th SLAC Summer Institute (SSI 2021)

Is the local Lorentz invariance of general relativity implemented by gauge bosons that have their own Yang-Mills-like action?

Not scheduled

20m

ZOOM videoconf (SLAC)

Speaker

Prof. Kevin Cahill (University of New Mexico)

Description

General relativity with fermions has two independent symmetries: general coordinate invariance and local Lorentz invariance. General coordinate invariance is implemented by the Levi-Civita connection and by Cartan's tetrads both of which have as their action the Einstein-Hilbert action. It is suggested here that local Lorentz invariance is implemented not by a combination of the Levi-Civita connection and Cartan's tetrads known as the spin connection, but by independent Lorentz bosons $L_{\phantom{ab}i}^{ab}$ that gauge the Lorentz group, that couple to fermions like Yang-Mills fields, and that have their own Yang-Mills-like action. Lorentz bosons couple to fermion number and generate a spin-dependent static potential that violates the weak equivalence principle. If a Higgs mechanism makes them massive, then the static potential also violates the inverse-square law. Experiments put upper bounds on the strength of such a potential for masses $m_L<20$ eV. These upper limits imply that Lorentz bosons, if they exist, are nearly stable and contribute to dark matter.

Presentation materials

PhysRevD.102.065011.pdf

poster_Cahill.pdf

Presentation video