Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions

Abstract

Meta-conformal transformations are constructed as sets of time-space transformations which are not angle-preserving but contain time- and space translations, time-space dilatations with dynamical exponent $z=1$ and whose Lie algebras contain conformal Lie algebras as sub-algebras. They act as dynamical symmetries of the linear transport equation in $d$ spatial dimensions. For $d=1$ spatial dimensions, meta-conformal transformations constitute new representations of the conformal Lie algebras, while for $d\ne 1$ their algebraic structure is different. Infinite-dimensional Lie algebras of meta-conformal transformations are explicitly constructed for $d=1$ and $d=2$ and they are shown to be isomorphic to the direct sum of either two or three centre-less Virasoro algebras, respectively. The form of co-variant two-point correlators is derived. An application to the directed Glauber-Ising chain with spatially long-ranged initial conditions is described.

1+32 pages, 5 figures, dedicated to the memory of V. Rittenberg. Final form. (several extensions with respect to precursor article arXiv:1711.05062)

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Cited by in corpus (3)

• Schrödinger symmetry: a historical review
• Boundedness of meta-conformal two-point functions in one and two spatial dimensions
• Superfield approach to higher derivative N=1 superconformal mechanics