Refining the Cutoff 3d Gravity / $T\bar{T}$ Correspondence

Understand

Pure gravity in AdS$_3$ is a theory of boundary excitations, most simply expressed as a constrained free scalar with an improved stress tensor that is needed to match the Brown--Henneaux central charge.

• Excising a finite part of AdS gives rise to a static gauge Nambu--Goto action for the boundary graviton.
• We show that this is the $T\bar{T}$ deformation of the infinite volume theory, as the effect of the improvement term on the deformed action can be absorbed into a field redefinition.
• The classical gravitational stress tensor is reproduced order by order by the $T\bar{T}$ trace equation.