PT Journal
AU Delhom, A
   Mariz, T
   Nascimento, JR
   Olmo, GJ
   Petrov, AY
   Porfirio, PJ
TI Spontaneous Lorentz symmetry breaking and one-loop effective action in the metric-affine bumblebee gravity
SO Journal of Cosmology and Astroparticle Physics
JI J. Cosmol. Astropart. Phys.
PY 2022
BP 018
EP 27pp
VL 07
IS 7
DI 10.1088/1475-7516/2022/07/018
LA English
DE gravity; modified gravity; quantum field theory on curved space; Quantum fields in curved spacetimes
AB The metric-affine bumblebee model in the presence of fermionic matter minimally coupled to the connection is studied. We show that the model admits an Einstein frame representation in which the matter sector is described by a non-minimal Dirac action without any analogy in the literature. Such non-minimal terms involve unconventional couplings between the bumblebee and the fermion field. We then rewrite the quadratic fermion action in the Einstein frame in the basis of 16 Dirac matrices in order to identify the coefficients for Lorentz/CPT violation in all orders of the non-minimal coupling xi. The exact result for the fermionic determinant in the Einstein frame, including all orders in xi, is also provided. We demonstrate that the axial contributions are at least of second order in the perturbative expansion of xi. Furthermore, we compute the one-loop effective potential within the weak field approximation.
ER