Meta-conformal invariance and the boundedness of two-point correlation functions

Abstract

The covariant two-point functions, derived from Ward identities in direct space, can be affected by consistency problems and can become unbounded for large time- or space-separations. This difficulty arises for several extensions of dynamical scaling, for example Schrödinger-invariance, conformal Galilei invariance or meta-conformal invariance, but not for standard ortho-conformal invariance. For meta-conformal invariance in 1+1 dimensions, these difficulties can be cured by going over to a dual space and an extension of these dynamical symmetries through the construction of a new generator in the Cartan sub-algebra. This provides a canonical interpretation of meta-conformally covariant two-point functions as correlators. Galilei-conformal correlators can be obtained from meta-conformal invariance through a simple contraction. In contrast, by an analogus construction, Schrödinger-covariant two-point functions are causal response functions. All these two-point functions are bounded at large separations, for sufficiently positive values of the scaling exponents.

arXiv commentLatex 2e, 11 pp, no figures, final form

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Cited by in corpus (8)

• Schrödinger symmetry: a historical review
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• Non-local meta-conformal invariance in diffusion-limited erosion
• Boundedness of meta-conformal two-point functions in one and two spatial dimensions
• Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• Meta-conformal algebras in $d$ spatial dimensions