All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method

TL;DR

This paper analytically calculates the critical exponents at all loop levels for a massless Lorentz-violating scalar field theory, revealing how Lorentz violation influences critical phenomena.

Contribution

It provides the first all-loop order calculation of critical exponents in a Lorentz-violating scalar field theory using the BPHZ renormalization method.

Findings

Lorentz violation affects critical exponents.

Explicit calculations up to next-to-leading order.

Proof by induction for all loop levels.

Abstract

We compute analytically the all-loop level critical exponents for a massless thermal Lorentz-violating O($N$) self-interacting $\lambda\phi^{4}$ scalar field theory. For that, we evaluate, firstly explicitly up to next-to-leading order and later in a proof by induction up to any loop level, the respective $\beta$-function and anomalous dimensions in a theory renormalized in the massless BPHZ method, where a reduced set of Feynman diagrams to be calculated is needed. We investigate the effect of the Lorentz violation in the outcome for the critical exponents and present the corresponding mathematical explanation and physical interpretation.