Three-loop field renormalization for scalar field theory with Lorentz violation

Abstract

Applying the counterterm method in minimal subtraction scheme we calculate the three-loop quantum correction to field anomalous dimension in a Lorentz-violating O($N$) self-interacting scalar field theory. We compute the Feynman diagrams using dimensional regularization and $\epsilon$-expansion techniques. As this approximation corresponds to a three-loop term, to our knowledge this is the first time in literature in which such a loop level is attained for a LV theory.

12 pages

References in corpus (6)

• Phenomenologically viable Lorentz-violating quantum gravity
• One-Loop Renormalization of Pure Yang-Mills with Lorentz Violation
• One-Loop Renormalization of the Electroweak Sector with Lorentz Violation
• One-Loop Renormalization of QCD with Lorentz Violation
• Mass Renormalization in Lorentz-violating Scalar Field Theory
• Callan-Symanzik method for $m$-axial Lifshitz points

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• Critical properties of scalar field theory with Lorentz violation: Exact treatment of Lorentz-violating mechanism
• All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method
• Universality hypothesis breakdown at one-loop order
• Asymptotic single-particle states and exact Lorentz-violating all-loop quantum corrections for scalar field theory
• Unconventional minimal subtraction and Callan-Symanzik methods for Lorentz-violating scalar field theories at all loop orders
• Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism
• 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