Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field Theory - Stefano Baiguera; Troels Harmark; Yang Lei; Ziqi Yan (Journal of High Energy Physics)
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) × 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. [1], where the geometry acquires an Ω-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.