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Register a new userOn the symmetry of $Tbar T$ deformed CFT
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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.
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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.
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 perturbative renormalization of the composite operators in the $Tbar T$-deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].
String theory on AdS$_3$ with NS-NS fluxes admits a solvable irrelevant deformation which is close to the $Tbar{T}$ deformation of the dual CFT$_2$. This consists of deforming the worldsheet action, namely the action of the $SL(2,mathbb{R})$ WZW model, by adding to it the operator $J^-bar{J}^-$, constructed with two Kac-Moody currents. The geometrical interpretation of the resulting theory is that of strings on a conformally flat background that interpolates between AdS$_3$ in the IR and a flat linear dilaton spacetime with Hagedorn spectrum in the UV, having passed through a transition region of positive curvature. Here, we study the properties of this string background both from the point of view of the low-energy effective theory and of the worldsheet CFT. We first study the geometrical properties of the semiclassical geometry, then we revise the computation of correlation functions and of the spectrum of the $J^-bar{J}^-$-deformed worldsheet theory, and finally we discuss how to extend this type of current-current deformation to other conformal models.
We present the quantum $kappa$-deformation of BMS symmetry, by generalizing the lightlike $kappa$-Poincare Hopf algebra. On the technical level, our analysis relies on the fact that the lightlike $kappa$-deformation of Poincare algebra is given by a twist and the lightlike deformation of any algebra containing Poincare as a subalgebra can be done with the help of the same twisting element. We briefly comment on the physical relevance of the obtained $kappa$-BMS Hopf algebra as a possible asymptotic symmetry of quantum gravity.
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