We revisit the late-time growth rate of various holographic complexity conjectures for neutral an... more We revisit the late-time growth rate of various holographic complexity conjectures for neutral and charged AdS black holes with single or multiple horizons in two dimensional (2D) gravity like Jackiw-Teitelboim (JT) gravity and JT-like gravity. For complexity-action conjecture, we propose an alternative resolution to the vanishing growth rate at late-time for general 2D neutral black hole with multiple horizons as found in the previous studies for JT gravity. For complexity-volume conjectures, we obtain the generic forms of late-time growth rates in the context of extremal volume and Wheeler-DeWitt volume by appropriately accounting for the black hole thermodynamics in 2D gravity.
The Journal of high energy physics/The journal of high energy physics, Mar 4, 2024
In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and U(1)... more In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and U(1) current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein's gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for U(1) current and stress tensor in the scalar and shear channels.
Double holography offers a profound understanding of the island formula by describing a gravitati... more Double holography offers a profound understanding of the island formula by describing a gravitational system on AdSd coupled to a conformal field theory on ℝ1,d−1, dual to an AdSd+1 spacetime with an end-of-the-world (EOW) brane. In this work, we extend the proposal in [12] by considering that the dual bulk spacetime has two EOW branes: one with a gravitational system and the other with a thermal bath. We demonstrate an equivalence between this proposal and the wedge holographic theory. We examine it in both Anti-de Sitter gravity and de Sitter gravity by calculating the entanglement entropy of the Hawking radiation. Finally, we employ the doubly holographic model to verify the formula for the entanglement entropy in a subregion within conformally flat spacetime.
In this work, we investigate the time evolution of the pseudo-(Rényi) entropy after local primary... more In this work, we investigate the time evolution of the pseudo-(Rényi) entropy after local primary operator quenches in 2D CFTs with $$ T\overline{T}/J\overline{T} $$ T T ¯ / J T ¯ -deformation. Using perturbation theory, we analyze the corrections to the second pseudo-Rényi entropy at the late time, which exhibit a universal form, while its early-time behavior is model-dependent. Moreover, we uncover nontrivial time-dependent effects arising from the first-order deformation of the kth pseudo-Rényi entropy at the late time. Additionally, drawing inspiration from the gravitational side, specifically the gluing of two cutoff AdS geometries, we investigate the kth pseudo-Rényi entropy for vacuum states characterized by distinct $$ T\overline{T} $$ T T ¯ -deformation parameters, as well as for primary states acting on different deformed vacuum states. Our findings reveal additional corrections compared to the results of pseudo-Rényi entropy for globally deformed vacuum states.
We study the rotation effects of the hot and dense QCD matter in a non-perturbative regime by the... more We study the rotation effects of the hot and dense QCD matter in a non-perturbative regime by the gauge/gravity duality. We use the gravitational model that is designated to match the state-of-the-art lattice data on the thermal properties of (2+1)-flavor QCD and predict the location of the critical endpoint and the first-order phase transition line at large baryon chemical potential without rotation. After introducing the angular velocity via a local Lorentz boost, we investigate the thermodynamic quantities for the system under rotation in a self-consistent way. We find that the critical temperature and baryon chemical potential associated with the QCD phase transition decrease as the angular velocity increases. Moreover, some interesting phenomena are observed near the critical endpoint. We then construct the 3-dimensional phase diagram of the QCD matter in terms of temperature, baryon chemical potential, and angular velocity. As a parallel investigation, we also consider the gra...
Since the definition of T T deformation in the curved Riemann surface is obstructive in the liter... more Since the definition of T T deformation in the curved Riemann surface is obstructive in the literature, we propose a way to do the deformation in the genus two Riemann surfaces by sewing prescription. We construct the correlation functions of conformal field theories (CFTs) on genus two Riemann surfaces with the T T deformation in terms of the perturbative CFT approach. Thanks to sewing construction to form higher genus Riemann surfaces from lower genus ones and conformal symmetry, we systematically obtain the first order T T correction to the genus two correlation functions in the T T deformed CFTs, e.g., partition function and one/higher-point correlation functions.
We study the rotation effects of the hot and dense QCD matter in a non-perturbative regime by the... more We study the rotation effects of the hot and dense QCD matter in a non-perturbative regime by the gauge/gravity duality. We use the gravitational model that is designated to match the state-of-the-art lattice data on the thermal properties of (2+1)-flavor QCD and predict the location of the critical endpoint and the first-order phase transition line at large baryon chemical potential without rotation. After introducing the angular velocity via a local Lorentz boost, we investigate the thermodynamic quantities for the system under rotation in a self-consistent way. We find that the critical temperature and baryon chemical potential associated with the QCD phase transition decrease as the angular velocity increases. Moreover, some interesting phenomena are observed near the critical endpoint. We then construct the 3-dimensional phase diagram of the QCD matter in terms of temperature, baryon chemical potential, and angular velocity. As a parallel investigation, we also consider the gravitational model of SU (3) pure gluon system, for which the 2-dimensional phase diagram associated with temperature and angular velocity has been predicted. The corresponding thermodynamic quantities with rotation are investigated.
Understanding the nature of quantum chromodynamics (QCD) matter is important but challenging due ... more Understanding the nature of quantum chromodynamics (QCD) matter is important but challenging due to the presence of non-perturbative dynamics under extreme conditions. We construct a holographic model describing the gluon sector of QCD at finite temperatures in the non-perturbative regime. The equation of state as a function of temperature is in good accordance with the lattice QCD data. Moreover, the Polyakov loop and the gluon condensation, which are proper order parameters to capture the deconfinement phase transition, also agree quantitatively well with the lattice QCD data. We obtain a strong first-order confinement/deconfinement phase transition at Tc = 276.5 MeV that is consistent with the lattice QCD prediction. Based on our model for a pure gluon hidden sector, we compute the stochastic gravitational waves and primordial black hole (PBH) productions from this confinement/deconfinement phase transition in the early Universe. The resulting stochastic gravitational-wave backgrounds are found to be within detectability in the International Pulsar Timing Array and Square Kilometre Array in the near future when the associated productions of PBHs saturate the current observational bounds on the PBH abundances from the LIGO-Virgo-Collaboration O3 data.
In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entr... more In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entropy in a free fermion theory on a torus with three typical deformations, e.g., TT deformation, local bilinear operator deformation, and mass deformation. For TT deformation, we find that the leading order correction of entanglement entropy is proportional to the expectation value of the undeformed modular Hamiltonian. As a check, in the high/low-temperature limit, the entanglement entropy coincides with that obtained by the replica trick in the literature. Following the same perturbative strategy, we obtain the entanglement entropy of the free fermion vacuum state up to second-order by inserting a local bilinear operator deformation in a moving mirror setting. In the uniformly accelerated mirror, the first-order and second-order correction of entanglement entropy vanishes in the late time limit. For mass deformation, we derive the entanglement entropy up to first-order deformation and comment on the second-order correction.
In this work, we investigate the quantum chaos in various T T -deformed SYK models with finite N ... more In this work, we investigate the quantum chaos in various T T -deformed SYK models with finite N , including the SYK 4 , the supersymmetric SYK 4 , and the SYK 2 models. We numerically study the evolution of the spectral form factor (SFF), the out-of-time ordered correlator (OTOC), and the Krylov complexity. We find that the characteristic evolution of the SFF, OTOC and K-complexity of both the SYK 4 and SSYK 4 models remains unchanged under the deformation, which implies that the properties of quantum chaos is preserved. We also identify a many-body localization behavior in the deformed SYK 2 model.
In this work we calculate the partition functions of N = 1 type 0A and 0B JT supergravity (SJT) o... more In this work we calculate the partition functions of N = 1 type 0A and 0B JT supergravity (SJT) on 2D surfaces of arbitrary genus with multiple finite cutoff boundaries, based on the TT deformed super-Schwarzian theories. In terms of SJT/matrix model duality, we compute the corresponding correlation functions in the TT deformed matrix model side by using topological recursion relations as well as the transformation properties of topological recursion relations under TT deformation. We check that the partition functions finite cutoff 0A and 0B SJT on generic 2D surfaces match the associated correlation functions in TT deformed matrix models respectively.
We study the anomalous dimensions of operators in the scalar sector of planar β-deformed ABJ(M) t... more We study the anomalous dimensions of operators in the scalar sector of planar β-deformed ABJ(M) theories. We show that the anomalous dimension matrix at two-loop order gives an integrable Hamiltonian acting on an alternating SU (4) spin chain with the spins at odd lattice sides in the fundamental representation and the spins at even lattices in the anti-fundamental representation. We get a set of β-deformed Bethe ansatz equations which give the eigenvalues of Hamiltonian of this deformed spin chain system. Based on our computations, we also extend our study to non-supersymmetric three-parameter γdeformation of ABJ(M) theories and find that the corresponding Hamiltonian is the same as the one in β-deformed case at two-loop level in the scalar sector.
We study the entanglement entropy of excited states in two-dimensional conformal field theories (... more We study the entanglement entropy of excited states in two-dimensional conformal field theories (CFTs). In particular, we consider excited states obtained by acting on a vacuum with primary operators. We show that the entanglement entropy increases by a finite constant amount under its time evolution. Moreover, in rational conformal field theories, we prove that this increase of the (both Renyi and von Neumann) entanglement entropy always coincides with the log of the quantum dimension of the primary operator.
The Journal of high energy physics/The journal of high energy physics, May 22, 2024
This paper investigates holographic torus correlators of generic operators at conformal infinity ... more This paper investigates holographic torus correlators of generic operators at conformal infinity and a finite cutoff within AdS 3 gravity coupled with a free scalar field. Using a near-boundary analysis and solving the gravitational boundary value problem, we solve Einstein's equation and calculate mixed correlators for massless and massive coupled scalar fields. The conformal Ward identity on the torus has been reproduced holographically, which can be regarded as a consistency check. Further, recurrence relations for a specific class of higher-point correlators are derived, validating AdS 3 /CFT 2 with non-trivial boundary topology. While the two-point scalar correlator is accurately computed on the thermal AdS 3 saddle, the higher-point correlators associated with scalar and stress tensor operators are explored.
As a generalization of entanglement entropy, pseudo entropy is not always real. The real-valued p... more As a generalization of entanglement entropy, pseudo entropy is not always real. The real-valued pseudo entropy has promising applications in holography and quantum phase transition. We apply the notion of pseudo-Hermiticity to formulate the reality condition of pseudo entropy. We find the general form of the transition matrix for which the eigenvalues of the reduced transition matrix possess real or complex pairs of eigenvalues. Further, we find a class of transition matrices for which the pseudo (Rényi) entropies are non-negative. Some known examples which give real pseudo entropy in quantum field theories can be explained in our framework. Our results offer a novel method to generate the transition matrix with real pseudo entropy. Finally, we show the reality condition for pseudo entropy is related to the Tomita-Takesaki modular theory for quantum field theory.
In this work, we investigate the quantum chaos in various $$ T\overline{T} $$ T T ¯ -deformed SYK... more In this work, we investigate the quantum chaos in various $$ T\overline{T} $$ T T ¯ -deformed SYK models with finite N, including the SYK4, the supersymmetric SYK4, and the SYK2 models. We numerically study the evolution of the spectral form factor (SFF), the out-of-time ordered correlator (OTOC), and the Krylov complexity. We find that the characteristic evolution of the SFF, OTOC and K-complexity of both the SYK4 and SSYK4 models remains unchanged under the deformation, which implies that the properties of quantum chaos is preserved. We also identify a many-body localization behavior in the deformed SYK2 model.
In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entr... more In this work, we perturbatively calculate the modular Hamiltonian to obtain the entanglement entropy in a free fermion theory on a torus with three typical deformations, e.g., $$ T\overline{T} $$ T T ¯ deformation, local bilinear operator deformation, and mass deformation. For $$ T\overline{T} $$ T T ¯ deformation, we find that the leading order correction of entanglement entropy is proportional to the expectation value of the undeformed modular Hamiltonian. As a check, in the high/low-temperature limit, the entanglement entropy coincides with that obtained by the replica trick in the literature. Following the same perturbative strategy, we obtain the entanglement entropy of the free fermion vacuum state up to second-order by inserting a local bilinear operator deformation in a moving mirror setting. In the uniformly accelerated mirror, the first-order and second-order correction of entanglement entropy vanishes in the late time limit. For mass deformation, we derive the entanglemen...
In this paper, we have studied the kink and antikink solutions in several neutral scalar models i... more In this paper, we have studied the kink and antikink solutions in several neutral scalar models in 1+1 dimension. We follow the standard approach to write down the leading order and the second order force between long distance separated kink and antikink. The leading order force is proportional to exponential decay with respect to the distance between the two nearest kinks or antikinks. The second order force have a similar behavior with the larger decay factor, namely 3 2. We make use of these properties to construct the kink lattice. The dynamics of the kink lattice with leading order force can be identified as ordinary nonperiodic Toda lattice. Also the periodic Toda lattice can be obtained when the number of kink lattice is even. The system of kink lattice with force up to the next order corresponds to a new specific deformation of Toda lattice system. There is no well study on this deformation in the integrable literatures.We found that the deformed Toda system are near integrable system, since the integrability are hindered by high order correction terms. Our work provides a effective theory for kink interactions and a new near or quasi integrable model.
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