Renormalization group approach for Lorentz-violating scalar field theory at all loop orders

TL;DR

This paper calculates the critical exponents for a Lorentz-violating scalar field theory at all loop orders, demonstrating scheme independence and providing both mathematical and physical insights into the results.

Contribution

It introduces a method to compute critical exponents in Lorentz-violating theories at all loop levels using a simplified diagram approach and scheme-independent results.

Findings

Critical exponents are identical across different renormalization schemes.

Explicit calculations up to next-to-leading order confirm all-loop results.

Mathematical and physical interpretations are provided for the scheme-independent results.

Abstract

We compute, both explicitly up to next-to-leading order and in a proof by induction for all loop levels, the critical exponents for thermal Lorentz-violating O($N$) self-interacting scalar field theory. They are evaluated in a massless theory renormalized at arbitrary external momenta, where a reduced number of Feynman diagrams is eeded. The results are presented and shown to be identical to that found previously in distinct theories renormalized at different renormalization schemes. At the end we give both mathematical explanation and physical interpretation for them based on coordinates redefinition techniques and symmetry ideas, respectively.