Effective action of the Horava theory: Cancellation of divergences

Abstract

We compute the one-loop effective action of the Horava theory, in its nonprojectable formulation. We take the quantization of the (2+1)-dimensional theory in the Batalin-Fradkin-Vilkovisky formalism, and comment on the extension to the (3+1) case. The second-class constraints and the appropriate gauge-fixing condition are included in the quantization. The ghost fields associated with the second-class constraints can be used to get the integrated form of the effective action, which has the form of a Berezinian. We show that all irregular loops cancel between them in the effective action. The key for the cancellation is the role of the ghosts associated with the second-class constraints. These ghosts form irregular loops that enter in the denominator of the Berezinian, eliminating the irregular loops of the bosonic nonghost sector. Irregular loops produce dangerous divergences; hence their cancellation is an essential step for the consistency of the theory. The cancellation of this kind of divergences is in agreement with the previous analysis done on the (2+1) quantum canonical Lagrangian and its Feynman diagrams.

v2: The extension to the (3+1) case has been expanded. Other disscusion added

References in corpus (12)

• Quantum Gravity at a Lifshitz Point
• Weighted power counting and Lorentz violating gauge theories. I: General properties
• Asymptotic freedom in Horava-Lifshitz gravity
• Lower-dimensional Horava-Lifshitz gravity
• Beta functions of (3+1)-dimensional projectable Horava gravity
• Horava gravity with mixed derivative terms
• Cancellation of divergences in the nonprojectable Horava theory
• Hamiltonian analysis of nonprojectable Hořava-Lifshitz gravity with $U(1)$ symmetry
• Asymptotic freedom in (3+1)-dimensional projectable Horava gravity: connecting ultraviolet to infrared
• BFV quantization of the nonprojectable 2+1 Horava theory
• BRST symmetry and unitarity of the Horava theory
• Quantum Lagrangian of the Horava theory and its nonlocalities

Cited by in corpus (4)

• Fractional Einstein-Gauss-Bonnet scalar field cosmology
• Renormalization of the nonprojectable Horava theory
• Casimir Effect of rough plates under a magnetic field in Hořava-Lifshitz theory
• Quantizing non-projectable Hořava gravity with Lagrangian path integral