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Register a new user$Tbar{T}$ and $Jbar{T}$ Deformations in Quantum Mechanics
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In this paper, we continue the study of $Tbar{T}$ deformation in $d=1$ quantum mechanical systems and propose possible analogues of $Jbar{T}$ deformation and deformation by a general linear combination of $Tbar{T}$ and $Jbar{T}$ in quantum mechanics. We construct flow equations for the partition functions of the deformed theory, the solutions to which yields the deformed partition functions as integral of the undeformed partition function weighted by some kernels. The kernel formula turns out to be very useful in studying the deformed two-point functions and analyzing the thermodynamics of the deformed theory. Finally, we show that a non-perturbative UV completion of the deformed theory is given by minimally coupling the undeformed theory to worldline gravity and $U(1)$ gauge theory.
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We explore the $Jbar{T}$ and $Tbar{J}$ deformations of two-dimensional field theories possessing $mathcal N=(0,1),(1,1)$ and $(0,2)$ supersymmetry. Based on the stress-tensor and flavor current multiplets, we construct various bilinear supersymmetric primary operators that induce the $Jbar{T}/Tbar{J}$ deformation in a manifestly supersymmetric way. Moreover, their supersymmetric descendants are shown to agree with the conventional $Jbar T /Tbar J$ operator on-shell. We also present some examples of $Jbar T /Tbar J$ flows arising from the supersymmetric deformation of free theories. Finally, we observe that all the deformation operators fit into a general pattern which generalizes the Smirnov-Zamolodchikov type composite operators.
We investigate the $Tbar{T}$ deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the $Tbar{T}$ deforming operator can be constructed as a supersymmetric descendant. Here we focus on $mathcal{N}=(1,0)$ and $mathcal{N}=(1,1)$ supersymmetry. As an example, we analyse in detail the $Tbar{T}$ deformation of a free $mathcal{N}=(1,0)$ supersymmetric action. We also argue that the link between $Tbar{T}$ and string theory can be extended to superstrings: by analysing the light-cone gauge fixing for superstrings in flat space, we show the correspondence of the string action to the $Tbar{T}$ deformation of a free theory of eight $mathcal{N}=(1,1)$ scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of $Tbar{T}$ deformations that have recently been discussed in the literature.
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 study thermodynamic aspects of a tractable toy model of holography for extremal Kerr black holes proposed in [arXiv:1806.10127]. On the gravity side, the theory can be described by the worldsheet action of string theory on a warped AdS$_3$ background supported by NS-NS flux. Once we turn on temperature, the deformed background is described by a black string solution of type IIB supergravity that features a locally warped AdS$_3$ factor. The dual field theory is conjectured to be a single-trace version of a $Jbar{T}$-deformed CFT at finite temperature. As evidence for the correspondence we show that the spectrum of strings winding on the deformed background agrees with the spectrum of $Jbar{T}$-deformed CFTs. Furthermore, we show that the gravitational charges of the black string match the averaged charges of a thermal ensemble in the dual field theory. Finally, we reproduce the Bekenstein-Hawking entropy of the black string from the microscopic density of states of $Jbar{T}$-deformed CFTs.
We consider the most general set of integrable deformations extending the $Tbar{T}$ deformation of two-dimensional relativistic QFTs. They are CDD deformations of the theorys factorised S-matrix related to the higher-spin conserved charges. Using a mirror version of the generalised Gibbs ensemble, we write down the finite-volume expectation value of the higher-spin charges, and derive a generalised flow equation that every charge must obey under a generalised $Tbar{T}$ deformation. This also reproduces the known flow equations on the nose.
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