In this work, we study the holographic entanglement entropy in AdS$_3$ gravity with the certain mixed boundary condition, which turns out to correspond to $T\bar{T}$-deformed 2D CFTs. By employing the Chern-Simons formalism and Wilson line technique, the holographic entanglement entropy in $T\bar{T}$-deformed BTZ black hole is obtained. We also get the same formula by calculating the RT surface. The holographic entanglement entropy agrees with the perturbation result derived from both $T\bar{T}$-deformed CFTs and cutoff AdS$_3$. Moreover, our result shows that the deformed entanglement entropy for large deformation parameter behaves like the entanglement entropy of CFT at zero temperature. We also consider the entanglement entropy of two intervals and study the effect of $T\bar{T}$ deformation on phase transition.
A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.
The Ryu-Takayanagi (RT) formula has been a key ingredient in our understanding of holography. Recent work on TT deformations has also boosted our understanding of holography away from the conformal boundary of AdS. In this short note, we aim to refine some recent work demonstrating the success of the RT formula in TT deformed theories. We emphasize general arguments that justify the use of the RT formula in general holographic theories that obey a GKPW-like dictionary. In doing so, we clarify subtleties related to holographic counterterms and discuss the implications for holography in general …
In this work, we derive an upper bound on energetic quantities, namely vacuum energy and free energy, for static solutions of Einstein-Scalar theory in four dimensional asymptotically locally Anti-de Sitter(AlAdS) spacetime with a nontrivial scalar potential where the scalar field mass parameter($m^2$) is equal to 0 or -2. This system is the holographic dual of strongly coupled conformal field theory(CFT) in three dimensions being deformed by a relevant or marginal scalar operator of conformal dimension $Δ=1, 2, 3$. The bound is derived from a purely gravitational perspective regardless of the…
The light-cone gauge approach to $T{\overline T}$ deformed models is generalised to models deformed by U(1) conserved currents $J^α$, $\widetilde J^α$, stress-energy tensor $T^α_β$, and their various quadratic combinations of the form $ε_{αβ} K_1^αK_2^β$. It is then applied to derive a ten-parameter deformed Hamiltonian for a system of scalars with an arbitrary potential, the flow equations for the Hamiltonian density, and the flow equations for the energy of the deformed model. The flow equations disagree with the ones recently proposed in arXiv:1903.07606. The results obtained are applied to…
Certain objects of conformal field theory, for example partition functions on the rectangle and the torus, and one-point functions on the torus, are either invariant or transform simply under the modular group, properties which should be preserved under the $T\overline T$ deformation. The formulation and proof of this statement in fact extents to more general functions such as $T\overline T$ deformed modular and Jacobi forms. We show that the deformation acts simply on their Mellin transform, multiplying it by a universal entire function. Finally we show that Maass forms on the torus are eigen…
Sharpening the holographic correspondence of Jackiw-Teitelboim (JT) gravity and its dual matrix model description at a finite radial cutoff $λ$ through the $T\overline{T}$ deformation is of interest. To proceed, we simplify the problem by considering the Airy model and deform Airy correlators in the same way as in $T\overline{T}$-deformed JT gravity. We use those correlators to compute the annealed and quenched free energies for both $λ> 0$ and $λ< 0$ from an integral representation of the replica trick. At the leading order in $λ$ and low temperatures, we confirm that the genus-zero quenched …
We study the partition function of a $T \overline{T}$-deformed version of Yang-Mills theory on the two-sphere. We show that the Douglas-Kazakov phase transition persists for a range of values of the deformation parameter, and that the critical area is lowered. The transition is of third order and also induced by instantons, whose contributions we characterize.
The surface/state correspondence suggests that the bulk co-dimensional two surface could be dual to the quantum state in the holographic conformal field theory(CFT). Inspired by the cutoff-AdS/$T\overline{T}$-deformed-CFT correspondence, we propose that the quantum states of two-dimensional $T\overline{T}$-deformed holographic CFT are dual to some particular surfaces in the AdS$_3$ gravity. In particular, the time slice of the cut-off surface is dual to the ground state of the $T\overline{T}$-deformed CFT. We examine our proposal by studying the entanglement entropy and quantum information met…
In this work, we study the holographic entanglement entropy of two dimensional $T\bar{T}$-deformed conformal field theory. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of New massive gravity, General minimal massive gravity, and Exotic general massive gravity. We also apply Song's prescription to obtain the entanglement entropy for deformed theories. In each cases, we find agreement between the results.
In this paper, we study the entanglement entropy of a single interval on a cylinder in two-dimensional $T\overline{T}$-deformed conformal field theory. For such case, the (Rényi) entanglement entropy takes a universal form in a CFT. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of the conformal perturbation theory. We find that the correction to the entanglement entropy is nonvanishing in the finite temperature case, while it is vanishing in the finite size case. For the deformed holographic large $c$ CFT, which is propos…
The geometerization of the renormalization group flow triggered by the $T\bar{T}$ deformation of large $c$ conformal field theories in two dimensions is presented. This entails the construction of the off shell Einstein-Hilbert action in three dimensions from said renormalization group flow. The crucial ingredient to this construction will be the encoding of general covariance in the emergent bulk theory in a very particular form of the Wess--Zumino consistency conditions. The utilisation of the local renormalization group, which requires putting the theory under consideration on an arbitrary …
We use the holographic methods to calculate the entanglement entropy for field theories modified by $T\bar{T}$ insertion. Based on the available holographic proposals, this calculation reduces to the holographic computations in AdS with finite cut-off. We perform a direct holographic calculation of the entanglement entropy for two dimensional deformed theory. By direct we mean the evaluation of the gravitational action in the bulk spacetime which has been reconstructed from a dual CFT$_2$ on $n$-sheeted Riemann surface as a finite cut-off boundary. We also apply Ryu-Takayanagi's prescription t…
We consider a certain ${\cal N}=1$ supersymmetric, $SO(3)\times SO(3)$ invariant, subsector of the $ω$-deformed family of $SO(8)$-gauged ${\cal N}=8$ four-dimensional supergravities. The theory contains two scalar fields and two pseudoscalar fields. We look for stationary points of the scalar potential, corresponding to AdS vacua in the theory. One of these, which breaks all supersymmetries but is nonetheless stable, is new. It exists only when $ω\ne 0$. We construct supersymmetric domain wall solutions in the truncated theory, and we give a detailed analysis of their holographic dual interpre…
Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory deformed by the irrelevant operator $T \overline{T}$. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough, Mezei and Verlinde. We also consider a one-parameter fami…
$\mathrm{T}\overline{\mathrm{T}}$ deformation was originally proposed as an irrelevant solvable deformation for 2d relativistic quantum field theories (QFTs). The same family of deformations can also be defined for integrable quantum spin chains which was first studied in the context of integrability in AdS/CFT. In this paper, we construct such deformations for yet another type of models, which describe a collection of particles moving in 1d and interacting in an integrable manner. The prototype of such models is the Lieb-Liniger model. This shows that such deformations can be defined for a ve…
In holography, the IR behavior of a quantum system at nonzero density is described by the near horizon geometry of an extremal charged black hole. It is commonly believed that for systems on $S^3$, this near horizon geometry is $AdS_2\times S^3 $. We show that this is not the case: generic static, nonspherical perturbations of $AdS_2\times S^3 $ blow up at the horizon, showing that it is not a stable IR fixed point. We then construct a new near horizon geometry which is invariant under only $SO(3)$ (and not $SO(4)$) symmetry and show that it is stable to $SO(3)$-preserving perturbations (but n…
In this paper, we consider a deformed AdS background and study effect of deformation parameter on the pair production rate of the Schwinger effect. The electrostatic potential is important for the pair production in the holographic Schwinger effect. In this paper, we analyze the electrostatic potential in a deformed AdS background and investigate the effect of deformation parameter which may be useful to test of AdS/QCD. In the case of zero temperature we find that larger value of the deformation parameter leads to a smaller value of separation length of the test particles on the probe. Also w…
We use the quantum null energy condition in strongly coupled two-dimensional field theories (QNEC2) as diagnostic tool to study a variety of phase structures, including crossover, second and first order phase transitions. We find a universal QNEC2 constraint for first order phase transitions with kinked entanglement entropy and discuss in general the relation between the QNEC2-inequality and monotonicity of the Casini-Huerta c-function. We then focus on a specific example, the holographic dual of which is modelled by three-dimensional Einstein gravity plus a massive scalar field with one free …
In this Letter, based on the notion of gauge/gravity duality, we compute $ q $ SYK spectra in the presence of Yang-Baxter (YB) deformations. The gravitational counterpart of this duality turns out to be the YB deformed Almheiri-Polchinski (AP) model embodied with hyperbolic potential for the dilaton. Following Kaluza-Klein reduction on $ (AdS_2)_η\times (S^1/ Z_2) $, we compute the deformed Green's function that reproduces the original $ q $ SYK spectrum in the limit of vanishing deformations.
The light-cone gauge approach to $T\overline{T}$ deformed models is used to derive the $T\overline{T}$ deformed matrix nonlinear Schrödinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the $T\overline{T}$ deformed nonlinear Schrödinger and Korteweg--de Vries equations are discussed in detail. The NLS soliton exhibits the recently discussed phenomenon of widening/narrowing width of particles under the $T\overline{T}$ deformation. However, whether the soliton's size is increasing or decreasing depends not only on the sign of the defor…
In this paper, we consider deformed STU model in four dimensions including both electric and magnetic charges. Using AdS/CFT correspondence, we study holographic superconductor and obtain transport properties like electrical and thermal conductivities. We obtain transport properties in terms of the black hole magnetic charge and interpret it as magnetic monopole of dual field theory. We find that presence of magnetic charge is necessary to have maximum conductivities, and existence of magnetic monopole with a critical charge (137 e) to reach the maximum superconductivity is important. Also, we…
We derive the geodesic equation for determining the Ryu-Takayanagi surface in $AdS_3$ deformed by single trace $μT \bar T + \varepsilon_+ J \bar T + \varepsilon_- T \bar J$ deformation for generic values of $(μ, \varepsilon_+, \varepsilon_-)$ for which the background is free of singularities. For generic values of $\varepsilon_\pm$, Lorentz invariance is broken, and the Ryu-Takayanagi surface embeds non-trivially in time as well as spatial coordinates. We solve the geodesic equation and characterize the UV and IR behavior of the entanglement entropy and the Casini-Huerta $c$-function. We comme…
We study $ \text{T}\overline{\text{T}} $ deformations of chiral bosons using the formalism due to Sen. For arbitrary numbers of left- and right-chiral bosons, we find that the $ \text{T}\overline{\text{T}} $-deformed Lagrangian can be computed in closed form, giving rise to a novel non-local action in Sen's formalism. We establish that at the limit of infinite $ \text{T}\overline{\text{T}} $ coupling, the equations of motion of deformed theory exhibits chiral decoupling. We then turn to a discussion of $ \text{T}\overline{\text{T}} $-deformed chiral fermions, and point out that the stress tens…
We show that the $T \overline{T}$ deformation of two-dimensional quantum field theory on $\mathrm{AdS}_2$ is well-defined and solvable at the quantum level. Flow equations for the energy spectrum and partition function are derived in analogy with the flat space case. As a non-trivial check, we perturbatively compute the deformed energy spectrum for the case of a free scalar field. We analyze the high energy density of states of the deformed theory and find a Hagedorn growth of states.
In this work the Vacuum Energy Density Problem or Dark Energy Problem is studied on the basis of the earlier results by the author within the scope of the Holographic Principle. It is demonstrated that the previously introduced deformed quantum field theory at a nonuniform lattice in the finite-dimensional hypercube is consistent with the Holographic Principle (Holographic Entropy Bound)in case the condition of the physical system's stability with respect to the gravitational collapse is met, or simply stated, the gravitational stability is constrained. The associated deformation parameter is …
We study strongly coupled mass-deformed-CFT on a fixed de Sitter spacetime in three dimensions via holography. We elucidate the global causal structure of the four-dimensional spacetime dual to the de Sitter invariant vacuum state. The conformal boundaries of de Sitter appear as spacelike defects sourced by the mass deformation, which extend into the bulk as curvature singularities in AdS. We compute all one- and two-point functions of the deformed-CFT stress tensor and a scalar operator order-by-order in the mass deformation for a simple holographic model. These correlation functions admit a …
On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT
Birla Institute of Technology and Science（比拉理工学院）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Centro de Estudios Científicos (CECs)（科学研究中心）；Universidad San Sebastián（圣塞巴斯蒂安大学）；Universidad Andres Bello（安德烈斯贝略大学）
We study the entanglement entropy (EE) and the Rényi entropy (RE) of multiple intervals in two-dimensional $T\overline{T}$-deformed conformal field theory (CFT) at finite temperature by field theoretic and holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a non-trivial consequence from the …
$T\overline{T}$-deformed two-dimensional quantum Maxwell theory on the torus is examined, taking into account nonperturbative effects in the deformation parameter $μ$. We study the deformed partition function solving the relevant flow equation at the level of individual flux sectors. Summing exactly the "instanton" series, we obtain a well-defined expression for the partition function at arbitrary $μ$. For $μ>0$, the quantum spectrum of the theory experiences a truncation, the partition function reducing to a sum over a finite set of positive-energy states. For $μ<0$ instead, the appearance of…
We study the $T\overline{T}$ deformation of two dimensional quantum field theories from a Hamiltonian point of view, focusing on aspects of the theory in Lorentzian signature. Our starting point is a simple rewriting of the spatial integral of the $T\overline{T}$ operator, which directly implies the deformed energy spectrum of the theory. Using this rewriting, we then derive flow equations for various quantities in the deformed theory, such as energy eigenstates, operators, and correlation functions. On the plane, we find that the deformation merely has the effect of implementing successive ca…
Quantum field theory in zero spatial dimensions has a rich infrared landscape and a universal ultraviolet, inverting the usual Wilsonian paradigm. For holographic theories this implies a rich landscape of asymptotically AdS$_2$ geometries. Isolating the interiors of these spacetimes suggests a study of the analog of the $T\overline{T}$ deformation in quantum mechanics, which we pursue here. An equivalent description of this deformation in terms of coupling to worldline gravity is proposed, and applications to quantum mechanical systems - including the Schwarzian theory - are studied.
We calculate quantum corrections to holographic entanglement entropy in the proposed duality between $T\bar{T}$-deformed holographic 2D CFTs and gravity in AdS$_{3}$ with a finite cutoff. We first establish the dictionary between the two theories by mapping the flow equation of the deformed CFT to the bulk Wheeler-DeWitt equation. The latter reduces to an ordinary differential equation for the sphere partition function, which we solve to find the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere. The entanglement entropy in the inverse central charge…
In this paper, minimal surface in $q$-deformed $AdS_5\times S^5$ with boundary a cusp is studied in detail. This minimal surface is dual to cusped Wilson loop in the dual field theory. We found that the area of the minimal surface has both logarithmic squared divergence and logarithmic divergence. The logarithmic squared divergence can not be removed by either Legendre transformation or the usual geometric substraction. We further make analytic continuation to the Minkowski signature %for the case without the jump and take the limit such that the two edges of the cusp become light-like and ext…
We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincare AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or $T \bar{T}$ deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be…
