Abstract
We study the TT 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 TT 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. This leads us to
define a class of non-local, “dressed” operators (including a dressed
stress tensor) which satisfy the same commutation relations as in the
undeformed theory. This further implies that on the plane, the deformed
theory retains its symmetry algebra, including conformal symmetry, if
the original theory is a CFT. On the cylinder the TT deformation is much
more non-trivial, but even so, correlation functions of certain dressed
operators are integral transforms of the original ones. Finally, we
propose a tensor network interpretation of our results in the context of
AdS/CFT.
Subject
General Physics and Astronomy
Cited by
8 articles.
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