Generic anisotropic Lifshitz scalar field theory: masslesslike massive minimal subtraction

TL;DR

This paper develops a minimal subtraction renormalization scheme for massive anisotropic Lifshitz scalar fields with O(N) symmetry, extending massless techniques and validating it through critical exponent calculations.

Contribution

It introduces a novel minimal subtraction method for massive Lifshitz scalar theories that simplifies calculations by discarding mass coefficient terms, applicable up to three loops.

Findings

Validated the method through three-loop critical exponent calculations

Confirmed the universality hypothesis in the Lifshitz scalar context

Provided a consistent minimal subtraction scheme similar to massless theories

Abstract

We formulate the simplest minimal subtraction version for massive $\lambda \phi^4$ scalar fields with $O(N)$ symmetry for generic anisotropic Lifshitz space-times. An appropriate partial$-p$ operation is applied in the bare two-point vertex function diagrams, which separates the original diagram into a sum of two different integrals which are the coefficients of the corresponding polynomials in the mass and external momentum. Within the proposed method, the coefficient of the mass terms can be discarded and we obtain a minimal subtraction method almost identical to the same scheme in the massless theory in {\it every external momentum/mass subspace}. We restrict our demonstration of the method up to three-loop order in the two-point vertex part. We verify the consistency of our method by a diagrammatic computation of static critical exponents, which validates the universality hypothesis.