Effective potentials in the Lifshitz scalar field theory

Abstract

We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling $z=2$, and show that the renormalization is possible without resort to the renormalization of the coupling constant due to the improvement of UV divergence. Moreover, the IR divergence can be also solved for the massless case of $m^2=0$, because of the absence of the logarithmic divergence. For a massive case, we obtain a condition for the symmetry breaking. Finally, we investigate whether the critical temperature can exist or not in this approximation. The physical consequences of the other logarithmic divergence free model is discussed.

14 pages, 4 figures

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• Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Horava-Lifshitz Cosmology
• Solutions to Horava Gravity
• Thermodynamics of Black Holes in Horava-Lifshitz Gravity
• Renormalization group in Lifshitz-type theories
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• Symmetry breaking and restoration in Lifshitz type theories
• Symmetry breaking and restoration for interacting scalar and gauge fields in Lifshitz type theories
• Black Holes and Thunderbolt Singularities with Lifshitz Scaling Terms
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• Mixed field theory
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• Ultraviolet properties of Lifshitz-type scalar field theories
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• Singularities of the Casimir Energy for Quantum Field Theories with Lifshitz Dimensions
• On the regularization of Lifshitz-type field theories
• Higher-derivative four-dimensional sine-Gordon model
• New dynamical realizations of the Lifshitz group