Conformal equations that are not Virasoro or Weyl invariant

Abstract

While the argument by Zamolodchikov and Polchinski suggests global conformal invariance implies Virasoro invariance in two-dimensional unitary conformal field theories with discrete dilatation spectrum, it is not the case in more general situations without these assumptions. We indeed show that almost all the globally conformal invariant differential equations in two dimensions are neither Virasoro invariant nor Weyl invariant. The only exceptions are the higher spin conservation laws, conformal Killing tensor equations and the Laplace equation of a conformal scalar.

arXiv comment18 pages, v2: appendix added

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Cited by in corpus (4)

• Revisiting the Conformally Soft Sector with Celestial Diamonds
• Scale without Conformal Invariance in Dipolar Ferromagnets
• Conformal Contact Terms and Semi-Local Terms
• On the Conformal Symmetry of Exceptional Scalar Theories