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Register a new userNote on the nonrelativistic $Tbar{T}$ deformation
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In this paper, we present our study on the $Tbar{T}$-deformation of non-relativistic complex scalar field theory. We find the closed form of the deformed Lagrangian by using the perturbation and the method of characteristics. Furthermore we compute the exact energy spectrum of the deformed free theory by using the Brillouin-Wigner perturbation theory in an appropriate regularization scheme.
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We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the $lambda Tbar T$ deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each field, with a Dirac-like string being attached at each infinitesimal step. The deformation then acts as a derivation on the whole operator algebra, satisfying the Leibniz rule. We derive an explicit equation which allows for the analysis of UV divergences, which may be absorbed into a non-local field renormalization to give correlation functions which are UV finite to all orders, satisfying a (deformed) operator product expansion and a Callan-Symanzik equation. We solve this in the case of a deformed CFT, showing that the Fourier-transformed renormalized two-point functions behave as $k^{2Delta+2lambda k^2}$, where $Delta$ is their IR conformal dimension. We discuss in detail deformed Noether currents, including the energy-momentum tensor, and show that, although they also become non-local, when suitably improved they remain finite, conserved and satisfy the expected Ward identities. Finally, we discuss how the equivalence of the $Tbar T$ deformation to a state-dependent coordinate transformation emerges in this picture.
We consider a gravitational perturbation of the Jackiw-Teitelboim (JT) gravity with an arbitrary dilaton potential and study the condition under which the quadratic action can be seen as a $Tbar{T}$-deformation of the matter action. As a special case, the flat-space JT gravity discussed by Dubovsky et al[arXiv:1706.06604 ] is included. Another interesting example is a hyperbolic dilaton potential. This case is equivalent to a classical Liouville gravity with a negative cosmological constant and then a finite $Tbar{T}$-deformation of the matter action is realized as a gravitational perturbation on AdS$_2$.
We study the $Tbar T$ deformation on a multi-quantum mechanical systems. By introducing the dynamical coordinate transformation, we obtain the deformed theory as well as the solution. We further study the thermo-field-double state under the $Tbar T$ deformation on these systems, including conformal quantum mechanical system, the Sachdev-Ye-Kitaev model, and the model satisfying Eigenstate Thermalization Hypothesis. We find common regenesis phenomena where the signal injected into one local system can regenerate from the other local system. From the bulk picture, we study the deformation on Jackiw-Teitelboim gravity governed by Schwarzian action and find that the regenesis phenomena here are not related to the causal structure of semi-classical wormhole.
We continue the study of a recently proposed solvable irrelevant deformation of an AdS$_3$/CFT$_2$ correspondence that leads in the UV to a theory with Hagedorn spectrum. This can be thought of as a single trace analog of the $Tbar{T}$-deformation of the dual CFT$_2$. Here we focus on the deformed worldsheet theory in presence of a conformal boundary. First, we compute the expectation value of a bulk primary operator on the disc geometry. We give a closed expression for such observable, from which we obtain the anomalous conformal dimension induced by the deformation. We compare the result with that coming from the computation of the 2-point correlation function on the sphere, finding exact agreement. We perform the computation using different techniques and making a comparative analysis of different regularization schemes to solve the logarithmically divergent integrals. This enables us to perform further consistency checks of our result by computing other observables of the deformed theory: We compute both the bulk-boundary 2-point and the boundary-boundary 2-point functions and are able to reproduce the anomalous dimensions of both boundary and bulk operators.
We study non-perturbative quantum aspects of $Tbar{T}$-deformation of a free $O(N)$ vector model by employing the large $N$ limit. It is shown that bound states of the original field appear and inevitably become negative-norm states. In particular, the bound states can be regarded as the states of the conformal mode in a gravitational theory, where the Liouville action is induced with the coefficient proportional to the minus of central charge. To make the theory positive-definite, some modification is required so as to preserve diffeomorphism invariance due to the Faddeev-Popov ghosts with a negative central charge.
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