Power-counting and Renormalizability in Lifshitz Scalar Theory

Abstract

We study the renormalizability in theories of a self-interacting Lifshitz scalar field. We show that although the statement of power-counting is true at one-loop order, in generic cases where the scalar field is dimensionless, an infinite number of counter terms are involved in the renormalization procedure. This problem can be avoided by imposing symmetries, the shift symmetry in the present paper, which allow only a finite number of counter terms to appear. The symmetry requirements might have important implications for the construction of matter field sectors in the Horava-Lifshitz gravity.

arXiv comment16 pages, 3 figures

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• Tree-Level Unitarity and Renormalizability in Lifshitz Scalar Theory
• Black Holes and Thunderbolt Singularities with Lifshitz Scaling Terms
• Stable Singularity-free Cosmological Solutions in non-projectable Horava-Lifshitz Gravity
• S-matrix Unitarity and Renormalizability in Higher Derivative Theories
• Matter scattering in $R_{\mu \nu }^2$ gravity and unitarity
• Thermodynamics and and phase transition of topological dilatonic Lifshitz-like black holes
• Perturbative $S$-matrix unitarity ($S^{†}S=1$) in $R_{\mu \nu }^2$ gravity
• High-energy properties of the graviton scattering in quadratic gravity
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Barboza-Alcaniz Equation of State Parametrization : Constraining the Parameters in Different Gravity Theories
• Euclidean Wormholes in Horava-Lifshitz Gravity
• Universal horizons and Hawking radiation in nonprojectable 2d Hořava gravity coupled with a non-relativistic scalar field
• Aspects of Black Holes in Gravitational Theories with Broken Lorentz and Diffeomorphism Symmetries
• Tree-Unitarity and renormalizability in Lifshitz-scaling theory -- as a toy model of Hořava's gravity theory
• New dynamical realizations of the Lifshitz group