Refining the cutoff 3d gravity/$$ T\overline{T} $$ correspondence

A bstract Pure gravity in AdS 3 is a theory of boundary excitations, most simply expressed as constrained free scalar with an improved stress tensor that needed to match the Brown-Henneaux central charge. Excising finite part gives rise static gauge Nambu-Goto action for graviton. We show this $$ T\overline{T} T ¯ deformation infinite volume theory, effect improvement term on deformed can be absorbed into field redefinition. The classical gravitational reproduced order by trace equation. calculate energy spectrum and find equation imposes sufficient constraints ordering ambiguities guarantee agreement light-cone prediction. correlation functions, however, are not completely fixed how both allow terms, we these undetermined total derivative terms Zamolodchikov’s point splitting definition operator.