Abstract
The Toverline{T} deformation of a relativistic two-dimensional theory results in a solvable gravitational theory. Deformed scattering amplitudes can be obtained from coupling the undeformed theory to the flat space Jackiw-Teitelboim (JT) gravity. We show that the JT description is applicable and useful also in finite volume. Namely, we calculate the torus partition function of an arbitrary matter theory coupled to the JT gravity, formulated in the first order (vielbein) formalism. The first order description provides a natural set of dynamical clocks and rods for this theory, analogous to the target space coordinates in string theory. These dynamical coordinates play the role of relational observables allowing to define a torus path integral for the JT gravity. The resulting partition function is one-loop exact and reproduces the Toverline{T} deformed finite volume spectrum.
Highlights
A family of S-matrices (1.1) can be interpreted as a trajectory in field theory space such that its tangent vector at each point is set by the T Toperator
We find that the T Tdeformed partition function is one-loop exact for any quantum field theory
We presented a derivation of the finite volume spectrum corresponding to the gravitationally dressed S-matrix (1.1) by a brute force evaluation of the torus partition function in the flat space JT gravity
Summary
A family of S-matrices (1.1) can be interpreted as a trajectory in field theory space such that its tangent vector at each point is set by the T Toperator. This description allows to calculate the effect of the deformation (1.1) on the finite volume spectrum of a theory compactified on a circle of circumference R. We see that the T Tdescription of the deformation (1.1) is definitely useful and provides new important insights into its properties It is rather different from the conventional ways to construct quantum theories, especially given that T Tis an irrelevant operator. The full action for the deformed theory takes the following form,
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