Boundedness of meta-conformal two-point functions in one and two spatial dimensions

Abstract

Meta-conformal invariance is a novel class of dynamical symmetries, with dynamical exponent z = 1, and distinct from the standard ortho-conformal invariance. The meta-conformal Ward identities can be directly read off from the Lie algebra generators, but this procedure implicitly assumes that the co-variant correlators should depend holomorphically on time-and space coordinates. Furthermore, this assumption implies un-physical singularities in the co-variant correlators. A careful reformulation of the global meta-conformal Ward identities in a dualised space, combined with a regularity postulate, leads to bounded and regular expressions for the co-variant two-point functions, both in d = 1 and d = 2 spatial dimensions.

Meta-Schrödinger invariance

“…Herein, R(t) ∈ SO(d) is a time-dependent rotation matrix and f, f, b, a are differentiable (vector) functions of their argument. Co-variant n-point functions are predicted as either correlators or responses, following from the extension of the Cartan sub-algebra[11,12,13,16].…”