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

TL;DR

This paper reformulates meta-conformal Ward identities to derive bounded, regular two-point functions in one and two spatial dimensions, addressing previous issues with unphysical singularities.

Contribution

It introduces a dualised space approach and a regularity postulate to obtain physically meaningful two-point functions in meta-conformal invariance.

Findings

Derived bounded two-point functions in 1D and 2D

Resolved unphysical singularities in correlators

Provided a new formulation of Ward identities

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.