$T\bar T + \Lambda_2$ from a 2d gravity path integral

Understand

We develop a two-dimensional gravity path integral formulation of the $T \bar T + \Lambda_2$ deformation of quantum field theory.

• This provides an exactly solvable generalization of the pure $T \bar T$ deformation that is relevant for de Sitter and flat space holography.
• The path integral sheds light on quantum aspects of these flows in curved space, most notably the Weyl anomaly, the operator relation for the trace of the energy-momentum tensor, and the renormalization of the composite $T \bar T$ operator.
• It also applies to both the Hagedorn and the holographic signs of such flows.