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Register a new user$Tbar{T}/Jbar{T}$-deformed WZW models from Chern-Simons AdS$_3$ gravity with mixed boundary conditions
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In this work we consider AdS$_3$ gravitational theory with certain mixed boundary conditions at spatial infinity. Using the Chern-Simons formalism of AdS$_3$ gravity, we find that these boundary conditions lead to non-trivial boundary terms, which, in turn, produce exactly the spectrum of the $Tbar{T}/Jbar{T}$-deformed CFTs. We then follow the procedure for constructing asymptotic boundary dynamics of AdS$_3$ to derive the constrained $Tbar{T}$-deformed WZW model from Chern-Simons gravity. The resulting theory turns out to be the $Tbar{T}$-deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a $U(1)$ gauge field associated to the current $J$, we obtain one type of the $Jbar T$-deformed WZW model, and show that its action can be constructed from the gravity side. These results provide a check on the correspondence between the $Tbar{T}/Jbar{T}$-deformed CFTs and the deformations of boundary conditions of AdS$_3$, the latter of which may be regarded as coordinate transformations.
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Recently, a variety of deformed $T^{1,1}$ manifolds, with which 2D non-linear sigma models (NLSMs) are classically integrable, have been presented by Arutyunov, Bassi and Lacroix (ABL) [arXiv:2010.05573]. We refer to the NLSMs with the integrable deformed $T^{1,1}$ as the ABL model for brevity. Motivated by this progress, we consider deriving the ABL model from a 4D Chern-Simons (CS) theory with a meromorphic one-form with four double poles and six simple zeros. We specify boundary conditions in the CS theory that give rise to the ABL model and derive the sigma-model background with target-space metric and anti-symmetric two-form. Finally, we present two simple examples 1) an anisotropic $T^{1,1}$ model and 2) a $G/H$ $lambda$-model. The latter one can be seen as a one-parameter deformation of the Guadagnini-Martellini-Mintchev model.
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.
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 propose a symmetry of $Tbar T$ deformed 2D CFT, which preserves the trace relation. The deformed conformal killing equation is obtained. Once we consider the background metric runs with the deformation parameter $mu$, the deformation contributes an additional term in conformal killing equation, which plays the role of renormalization group flow of metric. The conformal symmetry coincides with the fixed point. On the gravity side, this deformed conformal killing equation can be described by a new boundary condition of AdS$_3$. In addition, based on the deformed conformal killing equation, we derive that the stress tensor of the deformed CFT equals to Brown-Yorks quasilocal stress tensor on a finite boundary with a counterterm. For a specific example, BTZ black hole, we get $Tbar T$ deformed conformal killing vectors and the associated conserved charges are also studied.
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.
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