Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory

Abstract

We realize an explicit conformal mapping between the state and operator pictures in a class of (2+1)-dimensional non-Lorentzian field theories with SU(1,2)$\times$U(1) conformal symmetry. The state picture arises from null reducing four-dimensional relativistic conformal field theories on a three-sphere, yielding a non-Lorentzian geometry with the conformal Killing symmetry group SU(1,2). This is complementary to the operator picture recently studied by Lambert et al., where the geometry acquires an $\Omega$-deformation. We then use the geometric mapping between the two pictures to derive a correspondence between the generators. This provides a concrete realization of the state-operator correspondence in non-Lorentzian conformal field theories.

29+10 pages, 3 figures; v2, minor corrections; v3, journal version

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Cited by in corpus (1)

• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity