Critical properties of scalar field theory with Lorentz violation: Exact treatment of Lorentz-violating mechanism

Abstract

In this work, we compute analytically the infrared divergences of massless O($N$) self-interacting scalar field theories with Lorentz violation, which are exact in the Lorentz-violating $K_{\mu \nu }$ coefficients, for evaluating the corresponding next-to-leading order critical exponents. For that, we apply three distinct and independent field-theoretic renormalization group methods. We find that the outcomes for the critical exponents are the same in the three methods and, furthermore, are identical to their Lorentz invariant counterparts. We generalize the results for all loop levels by employing a general theorem arising from the exact procedure and give the corresponding physical interpretation.

arXiv comment14 pages, 21 figures

References in corpus (27)

• Lorentz-Violating Extension of the Standard Model
• Critical Phenomena and Renormalization-Group Theory
• Gravity, Lorentz Violation, and the Standard Model
• Noncommutative Field Theory and Lorentz Violation
• Nonstandard optics from quantum spacetime
• Quantum Spacetime Phenomenology
• Ultraviolet modifications of dispersion relations in effective field theory
• Matter-gravity couplings and Lorentz violation
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• One-Loop Renormalization of Lorentz-Violating Electrodynamics
• Exact calculation of the radiatively-induced Lorentz and CPT violation in QED
• Tests of Lorentz symmetry in the gravitational sector
• Cosmology and the Standard Model
• Renormalization of Scalar and Yukawa Field Theories with Lorentz Violation
• One-Loop Renormalization of the Electroweak Sector with Lorentz Violation
• Analogue Aharonov-Bohm effect in a Lorentz-violating background
• Search for anisotropic Lorentz invariance violation with γ-rays
• A new picture of the Lifshitz critical behavior
• Callan-Symanzik-Lifshitz approach to generic competing systems
• Mass Renormalization in Lorentz-violating Scalar Field Theory
• Critical behavior of generic competing systems
• Status and prospects for $CPT$ and Lorentz invariance violation searches in neutral meson mixing
• Callan-Symanzik method for $m$-axial Lifshitz points
• Three-loop field renormalization for scalar field theory with Lorentz violation
• Robustness of the O($N$) universality class
• Renormalization group approach for Lorentz-violating scalar field theory at all loop orders
• All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method

Cited by in corpus (6)

• Effective potential in Lorentz-breaking field theory models
• Diffeomorphism symmetry effect on the O(N ) universality class
• Influence of exact Lorentz-violating mechanism on the critical exponents for massive $q$-deformed $\lambda {\varphi }^4$ scalar field theory
• Exact Lorentz-violating $q$-deformed O($N$) universality class
• Influence of conformal symmetry on the amplitude ratios for O($N$) models
• NLO critical exponents of O($N$) lambda ${\varphi }^4$ scalar field theories in curved spacetime