Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories

Abstract

Abstract In this work we evaluate analytically the ultraviolet divergences of Lorentz-violating massive O(N) $$\lambda \phi ^{4}$$ λ ϕ 4 scalar field theories, which are exact in the Lorentz-violating mechanism, firstly explicitly at next-to-leading order and latter at any loop level through an induction procedure based on a theorem following from the exact approach, for computing the corresponding critical exponents. For attaining that goal, we employ three different and independent field-theoretic renormalization group methods. The results found for the critical exponents show that they are identical in the three distinct methods and equal to their Lorentz-invariant counterparts. Furthermore, we show that the results obtained here, based on the single concept of loop order of the referred terms of the corresponding $$\beta $$ β -function and anomalous dimensions, reduce to the ones obtained through the earlier non-exact approach based on a joint redefinition of the field and coupling constant of the theory, in the appropriate limit.