Generic anisotropic Lifshitz scalar field theory: New massive minimal subtraction

Abstract

We formulate the simplest minimal subtraction version for massive scalar fields with O(N) symmetry for generic anisotropic Lifshitz spacetimes. We introduce the simplest geometric concepts to define it as a special manifold. Then we restrict ourselves to flat Euclidean spaces. 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 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 its consistency through a diagrammatic computation of static critical exponents, which validates the universality hypothesis.