Lorentz symmetry violating Lifshitz-type field theories
arXiv:2209.11060 · doi:10.1142/S0217732322502030
Abstract
We discuss the ultraviolet sector of 3+1 dimensional Lifshitz-type anisotropic higher derivative scalar, fermion and gauge field theories, with anisotropy exponent z=3 and with explicit breaking of Lorentz symmetry. By discarding from the action all momentum dependent vertex operators, which is essential to avoid phenomenologically unacceptable deformations of the light cone, we find that renormalizable scalar self-interaction and Yukawa-like couplings are, in general, asymptotically free. However, the requirement of cancelling momentum dependent vertex operators is incompatible with gauge symmetry and, therefore, for this kind of theories, gauge symmetry as well as Lorentz symmetry are recovered only as emergent properties below some energy scale M, that must be constrained from experiments. The quantum corrections to the scalar mass and their impact on the hierarchy problem are also analyzed.
arXiv comment13 pages, 1 figure
References in corpus (32)
- Quantum Gravity at a Lifshitz Point
- Avoiding Dark Energy with 1/R Modifications of Gravity
- Living with Ghosts
- Lorentz invariance and quantum gravity: an additional fine-tuning problem?
- Quantum-Gravity Analysis of Gamma-Ray Bursts using Wavelets
- Quantum Criticality and Yang-Mills Gauge Theory
- Renormalization of Horava Gravity
- Renormalization of Lorentz violating theories
- Field Theory at a Lifshitz Point
- Renormalization group in Lifshitz-type theories
- Ostrogradski Formalism for Higher-Derivative Scalar Field Theories
- Lifshitz-type Quantum Field Theories in Particle Physics
- Robust Constraint on Lorentz Violation Using Fermi-LAT Gamma-Ray Burst Data
- Hořava gravity is asymptotically free (in 2+1 dimensions)
- Asymptotically free four-fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point
- Higher-derivative operators and effective field theory for general scalar-tensor theories
- Towards the renormalization group flow of Horava gravity in dimensions
- On the effective potential for Horava-Lifshitz-like theories
- On Higher Spatial Derivative Field Theories
- Beta functions of (3+1)-dimensional projectable Horava gravity
- On Ward Identities in Lifshitz-like Field Theories
- Effective potentials in the Lifshitz scalar field theory
- Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order
- Isotropic Lifshitz point in the O(N) Theory
- On the effective potential for Horava-Lifshitz-like theories with the arbitrary critical exponent
- Isotropic Lifshitz critical behavior from the functional renormalization group
- Indications of isotropic Lifshitz points in four dimensions
- Topological phase transitions in four dimensions
- Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory
- Isotropic Lifshitz Scaling in four dimensions
- Ultraviolet properties of Lifshitz-type scalar field theories
- Horava-Lifshitz Type Quantum Field Theory and Hierarchy Problem