Exact Lorentz-violating $q$-deformed O($N$) universality class

TL;DR

This paper investigates how exact Lorentz-violating symmetry affects quantum corrections to critical exponents in massless $q$-deformed O(N) scalar field theories, finding that Lorentz violation does not alter the critical exponents, supporting universality.

Contribution

It demonstrates that Lorentz-violating $q$-deformed critical exponents are identical to Lorentz-invariant ones across multiple renormalization methods, extending results to all loop orders.

Findings

Lorentz-violating and Lorentz-invariant $q$-deformed critical exponents are identical.

The results are consistent across three different renormalization group methods.

The universality hypothesis holds despite Lorentz symmetry breaking.

Abstract

We examine the influence of exact Lorentz-violating symmetry mechanism on the radiative quantum corrections to the critical exponents for massless $q$-deformed O($N$) $\lambda\phi^{4}$ scalar field theories. For that, we employ three different and independent field-theoretic renormalization group methods for computing analytically the $q$-deformed critical exponents up to next-to-leading order. Then we generalize the former finite loop level results for any loop order. We show that the Lorentz-violating $q$-deformed critical exponents, obtained through the three methods, turn out to be identical and furthermore the same as their Lorentz-invariant $q$-deformed ones. We argue that this result is in accordance with the universality hypothesis.