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

TL;DR

This paper analytically computes the critical exponents of Lorentz-violating scalar field theories, demonstrating they match Lorentz-invariant results across multiple renormalization methods, and generalizes findings to all loop levels.

Contribution

It provides an exact analytical treatment of Lorentz-violating effects on critical exponents, confirming their invariance and extending results to all loop orders.

Findings

Critical exponents are identical to Lorentz-invariant cases.

Results are consistent across three different renormalization methods.

General theorem extends findings to all loop levels.

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.