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Register a new userHeating up holography for single-trace $Jbar{T}$ deformations
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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.
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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.
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.
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.
In this work, we continue our study of string theory in the background that interpolates between $AdS_3$ in the IR to flat spacetime with a linear dilaton in the UV. The boundary dual theory interpolates between a CFT$_2$ in the IR to a certain two-dimensional Little String Theory (LST) in the UV. In particular, we study emph{computational complexity} of such a theory through the lens of holography and investigate the signature of non-locality in the short distance behavior of complexity. When the cutoff UV scale is much smaller than the non-locality (Hagedorn) scale, we find exotic quadratic and logarithmic divergences (for both volume and action complexity) which are not expected in a local quantum field theory. We also generalize our computation to include the effects of finite temperature. Up to second order in finite temperature correction, we do not any find newer exotic UV-divergences compared to the zero temperature case.
The holographic representation of the entanglement entropy of four dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the holographic representation are calculated by a method which does not require the solution of the equations of motion or a cut off. The two calculations disagree for rather generic geometries. The reasons for the disagreement are analyzed.
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