On the predictive power of Local Scale Invariance

TL;DR

This paper critically examines Local Scale Invariance (LSI), questioning its predictive power by showing it can reproduce any two-point correlator through suitable representations, thus challenging its universality claims.

Contribution

The work demonstrates that LSI's predictions for two-point functions are not unique, suggesting the theory's predictive content may be fundamentally limited.

Findings

LSI can reproduce any two-point correlator with an appropriate generator representation.

This ability questions the predictive power of LSI for anisotropic critical phenomena.

The paper calls for a reassessment of LSI's role in describing universal scaling functions.

Abstract

Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena designed in the spirit of conformal invariance. For a given representation of its generators it makes non-trivial predictions about the form of universal scaling functions. In the past decade several representations have been identified and the corresponding predictions were confirmed for various anisotropic critical systems. Such tests are usually based on a comparison of two-point quantities such as autocorrelation and response functions. The present work highlights a potential problem of the theory in the sense that it may predict any type of two-point function. More specifically, it is argued that for a given two-point correlator it is possible to construct a representation of the generators which exactly reproduces this particular correlator. This observation calls for a critical examination of the predictive content of the theory.