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2020

On the flow of states under $T\overline{T}$

Kruthoff, Jorrit, Parrikar, Onkar

Understand

We study the $T\overline{T}$ deformation of two dimensional quantum field theories from a Hamiltonian point of view, focusing on aspects of the theory in Lorentzian signature.

Our starting point is a simple rewriting of the spatial integral of the $T\overline{T}$ operator, which directly implies the deformed energy spectrum of the theory.
Using this rewriting, we then derive flow equations for various quantities in the deformed theory, such as energy eigenstates, operators, and correlation functions.
On the plane, we find that the deformation merely has the effect of implementing successive canonical/Bogoliubov transformations along the flow.