Lifshitz scaling to Lorentz-violating high derivative operator and gamma-ray bursts

Abstract

In this work we have used a Hořava-Lifshitz scaling to rewrite a Lorentz-violating higher-order derivative electrodynamics controlled by a background four-vector nµ. The photon propagator was obtained and we have analyzed the dispersion relation and the observational results of gammaray burst (GRB) experiments were used. The limits of the critical exponent were discussed in the light of the GRB data and the physical implications were compared with the current GRBLorentz-invariance-violation literature. We show that the bound for the Lorentz-violating coupling for dimension-six operators, obtained from a Hořava-Lifshitz scaling, is eight orders of magnitude better than the result found without considering a Hořava-Lifshitz scaling, also this bound is nearby one, which is expected to be relevant phenomenologically.

Black brane in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity

“…This happens as the critical exponent assumes z ± = (3 ± √ 13)/2, or approximately, z − ≃ −0.3 or z + ≃ 3.3. Non integer critical exponents have appeared in previous studies, e.g., [33,[48][49][50][51] -and references therein. Specially in [48,49] the authors argue that although the Lifshitz critical exponents in the action of a quantum field theory developing Lifshitz symmetry are assumed to be integer, there is no such limitation indeed since the obtained dispersion relation in the Hamiltonian density associated with the quantized theory shows the exact analytic continuation to non integer values of z.…”

Lorentz-violating dimension-five operator contribution to the black body radiation

“…Here R HLP = Λ HL M P with M P = 1.22 × 10 19 GeV , and Λ HL is the Horava-Lifshitz energy scale. As pointed in [18], this ratio can be considered as R HLP ≈ 10 −9 , unveiling a new route for explicitly breaking supersymmetry without reintroducing fine-tuning [18][19][20]. Therefore, the previous constraint lead us to investigate effects of the Horava-Lifshitz crossover scale at the order Λ HL ≈ 10 10 GeV , which follows the restrictions mentioned in [19].…”

“…The Lifshitz-scaling to modified dispersion relation is given by [18] where z is the Horava-Lifshitz critical exponent. Here R HLP = Λ HL M P with M P = 1.22 × 10 19 GeV , and Λ HL is the Horava-Lifshitz energy scale.…”

“…There is also a relationship between the Lorentz symmetry breaking parameter and the Lifshitz critical exponent [18] that readsξ (z) = 1.02 × 10 28 z−41 2.9 2 z − 0.81 2 z .…”

Induction of the Lorentz-violating effective actions in quantum electrodynamics

“…(2) and Eqs. (3a) -(3b) to address the specific problem of radiatively inducing some LIV effective actions such as CPT-odd Chern-Simons-like [17,18], CPT-even aether-like [42] and CPT-odd extensions with higher order derivatives [43][44][45][46], given respectively as…”