Lifshitz critical points meet Zamolodchikov perturbation theory

A bstract Critical points of classical and quantum lattice models are often described by scale-invariant Lifshitz theories which are anisotropic in the continuum limit, as characterized by a dynamical critical exponent z ≠ 1. This type of critical behavior can in principle be studied by deforming ordinary z = 1 conformal field theories (CFTs) by relevant vector operators breaking the rotational/Lorentz symmetry. In this short note, we consider a two-dimensional system of coupled minimal model CFTs $$ {\mathcal{M}}_{m,m+1} $$ M m , m + 1 which realizes this perspective in a controlled fashion via Zamolodchikov’s large m expansion. The model turns out to exhibit interesting properties, including a manifold of interacting Lifshitz fixed points and emergent rotational symmetry in the infrared.