arXiv subjects

Jie-qiang Wu

Publications and source records attributed to Jie-qiang Wu.

At least 19 recordsLinked to original sources

arXiv2026

Canonical quantization of the Pais-Uhlenbeck oscillator with a higher-derivative perturbation: a covariant phase space approach

In this paper, we apply the covariant phase space formalism to the perturbative canonical quantization of the Pais-Uhlenbeck oscillator, with the acceleration-squared term treated as a perturbation. We quantize this model by constructing the symplectic form on the low-energy solution space. We then compute the energy spectrum and the unequal-time commutator in a perturbative way, and obtain the results that agree with the expansion of the exact low-energy theory. The perturbation method bypasses the standard Ostrogradsky construction and naturally decouples the Ostrogradsky ghost. This work extends our previous perturbative quantization scheme to genuine higher-derivative theories.

quant-ph↗

arXiv2026

Canonical quantization for effective theories with perturbations altering degrees of freedom: a covariant phase space approach

The standard approach to canonical quantization encounters difficulties in dealing with perturbations that alter the kinetic structure of unperturbed theories. We show that the covariant phase space formalism provides a natural and technically efficient way to circumvent this obstruction. We illustrate the method with an exactly solvable model: a two-dimensional non-relativistic charged particle moving in a magnetic field and a harmonic confining potential, with its kinetic energy viewed as a perturbation. We quantize this model with covariant phase space formalism by constructing the solution perturbatively. We then calculate the energy spectrum and the unequal-time commutators of this model, and obtain the results that agree with the expansion of the exact theory. The procedure developed here is intended to serve as a systematic framework for the canonical quantization of more complex effective theories with higher-derivative or velocity-dependent perturbations.

hep-th↗

arXiv2026

The identification between the bulk and boundary conserved quantities

By using Wald formalism, we show that the identification between the bulk and boundary conserved quantities induced by the perturbation of generic non-electromagnetic matter field holds not only on top of the asymptotically flat stationary spacetimes but also on top of the asymptotically AdS stationary ones. We further show that such an identification reduces to the familiar form for the test point particle by viewing it as the limiting case of general matter.

hep-th↗

arXiv2025

A further support for the statement that the action of the HRT-area generates a kink transformation in the pure AdS$_3$ gravity

It is stated that the action of the Hubeny-Rangamani-Takayanagi (HRT) area, which is viewed as an observable, generates a kink transformation in gravity. In this paper, we provide a further support for the kink transformation statement by performing a relevant computation. Specifically, by acting the kink transformation to the boundary stress tensor, we compute the bracket between the HRT area with the boundary stress tensor. Here we represent the boundary stress tensor in terms of initial data on the Cauchy surface under holographic renormalization. Our computation reproduces the same result as the one in arXiv:2203.04270 derived from a different approach.

hep-th↗

arXiv2025

An Interpretation for the Equivalence of Two Holographic Computations of the Butterfly Velocity with the Canonical Formalism of Gravity

In this paper, we revisit the equivalence of two holographic computations of the butterfly velocity: the computation with the shock wave solution and the computation with the entanglement wedge reconstruction. We provide an interpretation for the equivalence of the two computations with the canonical formalism of gravity. Specifically, by taking use of the canonical formalism, we reformulate both computations into the ones with a similar form. Here, in both reformulated computations, the butterfly velocity is computed from applying a given set of initial data into the constraint equations. And the sets of initial data of both computations have a similar structure. We then interpret the equivalence of the two computations as from the similar form of the reformulated computations.

hep-th↗

arXiv2024

An Observable in Classical Pure AdS3 Gravity: the Twist along a Geodesic

In this paper, we consider a little-studied observable in classical pure AdS3 gravity: the twist along a geodesic. The motivation is that the twist only supports on the geodesic so may be a candidate element in the center of the algebra in either entanglement wedge associated to the geodesic. We study the properties of the twist and get the following results. First, we get the system's evolution generated by the twist, which exhibits a relative shift along the geodesic. Second, we show that the twist commutes with the length of the same geodesic, which supports the proposal that the twist is a candidate element in the center.

hep-th↗

arXiv2024

Link-area commutators in AdS${}_3$ area-networks

Random tensor networks (RTNs) have proved to be fruitful tools for modelling the AdS/CFT correspondence. Due to their flat entanglement spectra, when discussing a given boundary region $R$ and its complement $\bar R$, standard RTNs are most analogous to fixed-area states of the bulk quantum gravity theory, in which quantum fluctuations have been suppressed for the area of the corresponding HRT surface. However, such RTNs have flat entanglement spectra for all choices of $R, \bar R,$ while quantum fluctuations of multiple HRT-areas can be suppressed only when the corresponding HRT-area operators mutually commute. We probe the severity of such obstructions in pure AdS$_3$ Einstein-Hilbert gravity by constructing networks whose links are codimension-2 extremal-surfaces and by explicitly computing semiclassical commutators of the associated link-areas. Since $d=3,$ codimension-2 extremal-surfaces are geodesics, and codimension-2 `areas' are lengths. We find a simple 4-link network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT surface for which all link-areas commute. However, the algebra generated by the link-areas of more general networks tends to be non-Abelian. One such non-Abelian example is associated with entanglement-wedge cross sections and may be of more general interest.

hep-th↗

arXiv2022

Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim Gravity

In this paper we use the covariant Peierls bracket to compute the algebra of a sizable number of diffeomorphism-invariant observables in classical Jackiw-Teitelboim gravity coupled to fairly arbitrary matter. We then show that many recent results, including the construction of traversable wormholes, the existence of a family of $SL(2,\mathbb{R})$ algebras acting on the matter fields, and the calculation of the scrambling time, can be recast as simple consequences of this algebra. We also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the "typical state" versions of the firewall paradox. Unlike the "Schwarzian" or "boundary particle" formalism, our techniques involve no unphysical degrees of freedom and naturally generalize to higher dimensions. We do a few higher-dimensional calculations to illustrate this, which indicate that the results we obtain in JT gravity are fairly robust.

hep-th↗

arXiv2020

Covariant phase space with boundaries

The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity "$B$", whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving $B$ emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the Poisson bracket on covariant phase space directly coincides with the Peierls bracket, without any need for non-covariant intermediate steps, and we discuss possible implications for the entropy of dynamical black hole horizons.

hep-th↗

arXiv2019

Thermal Conformal Blocks

We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations related to AdS Witten diagrams. We give an analytic formula for the scalar conformal block in terms of generalized hypergeometric functions. As an application, we deduce an asymptotic formula for the three-point coeffcients of primary operators in the limit where two of the operators are heavy.

hep-th↗

arXiv2017

Witten Diagrams for Torus Conformal Blocks

We give a holographic description of global conformal blocks in two dimensional conformal field theory on the sphere and on the torus. We show that the conformal blocks for one-point functions on the torus can be written as Witten diagrams in thermal AdS. This is accomplished by deriving a general conformal Casimir equation for global conformal blocks, and showing that Witten diagrams obey the same equation. We study the semi-classical limit of n-point conformal blocks, and show that these equal the action of a network of bulk world-lines obeying appropriate geodesic equations. We give an alternate description in the Chern-Simons formulation of 3D gravity, where the conformal blocks are described by networks of Wilson lines, and argue that these formulations are equivalent.

hep-th↗

arXiv2016

Holographic Description of 2D Conformal Block in Semi-classical Limit

In this paper, we study the holographic descriptions of the conformal block of heavy operators in two-dimensional large c conformal field theory. We consider the case that the operators are pairwise inserted such that the distance between the operators in a pair is much smaller than the others. In this case, each pair of heavy operators creates a conical defect in the bulk. We propose that the conformal block is dual to the on-shell action of three dimensional geometry with conical defects in the semi-classical limit. We show that the variation of the on-shell action with respect to the conical angle is equal to the length of the corresponding conical defect. We derive this differential relation on the conformal block in the field theory by introducing two extra light operators as both the probe and the perturbation. Our study also suggests that the area law of the holographic Renyi entropy must holds for a large class of states generated by a finite number of heavy operators insertion.

hep-th↗

arXiv2016

Holographic Entanglement Entropy For a Large Class of States in 2D CFT

In this paper, we study the entanglement entropy in a large class of states of two-dimensional conformal field theory in the the large central charge limit. This class of states includes the states created by the insertion of a finite number of local heavy operators. By using the monodromy analysis, we obtain the leading order entanglement entropy for the general state. We show that it is exactly captured by the Ryu-Takayanagi formula, by using the Wilsonian line prescription in the Chern-Simons formulation of the AdS$_3$ gravity.

hep-th↗

arXiv2016

Higher spin entanglement entropy at finite temperature with chemical potential

It is generally believed that the semiclassical AdS$_3$ higher spin gravity could be described by a two dimensional conformal field theory with ${\cal{W}}$-algebra symmetry in the large central charge limit. In this paper, we study the single interval entanglement entropy on the torus in the CFT with a ${\cW}_3$ deformation. More generally we develop the monodromy analysis to compute the two-point function of the light operators under a thermal density matrix with a ${\cW}_3$ chemical potential to the leading order. Holographically we compute the probe action of the Wilson line in the background of the spin-3 black hole with a chemical potential. We find exact agreement.

hep-th↗

arXiv2015

Large Interval Limit of Rényi Entropy At High Temperature

In this paper, we propose a novel expansion to compute the large interval limit of the Rényi entropy of 2D CFT at high temperature. Via the replica trick, the single interval Rényi entropy of 2D CFT at finite temperature could be read from the partition function on $n$-sheeted torus connected with each other along a branch cut. We calculate the partition function by inserting a complete basis across the branch cut. Because of the monodromy condition across the branch cut in the large interval limit, the basis of the states should be the ones in the twist sector. We study the twist sector of a general module of CFT and find that there is an one-to-one correspondence between the twist sector states and the normal sector states. As an application, we revisit the non-compact free scalar theory and discuss the large interval limit of the Rényi entropy of this theory by using our proposal. We find complete agreement in the leading and next-leading orders with direct expansion of the exact partition function. Moreover, we prove the relation (\ref{th}) between thermal entropy and the entanglement entropy for a generic CFT with discrete spectrum.

hep-th↗

arXiv2015

Holographic Calculation for Large Interval Rényi Entropy at High Temperature

In this paper, we study the holographic Rényi entropy of a large interval on a circle at high temperature for the two-dimensional conformal field theory (CFT) dual to pure AdS$_3$ gravity. In the field theory, the Rényi entropy is encoded in the CFT partition function on $n$-sheeted torus connected with each other by a large branch cut. As proposed by Chen and Wu [Large interval limit of Rényi entropy at high temperature, arXiv:1412.0763], the effective way to read the entropy in the large interval limit is to insert a complete set of state bases of the twist sector at the branch cut. Then the calculation transforms into an expansion of four-point functions in the twist sector with respect to $e^{-\frac{2πTR}{n}}$. By using the operator product expansion of the twist operators at the branch points, we read the first few terms of the Rényi entropy, including the leading and next-to-leading contributions in the large central charge limit. Moreover, we show that the leading contribution is actually captured by the twist vacuum module. In this case by the Ward identity the four-point functions can be derived from the correlation function of four twist operators, which is related to double interval entanglement entropy. Holographically, we apply the recipe in [T. Faulkner, The entanglement Rényi entropies of disjoint intervals in AdS/CFT, arXiv:1303.7221] and [T. Barrella et al., Holographic entanglement beyond classical gravity, J. High Energy Phys. 09 (2013) 109] to compute the classical Rényi entropy and its one-loop quantum correction, after imposing a new set of monodromy conditions. The holographic classical result matches exactly with the leading contribution in the field theory up to $e^{-4πTR}$ and $l^6$, while the holographical one-loop contribution is in exact agreement with next-to-leading results in field theory up to $e^{-\frac{6πTR}{n}}$ and $l^4$ as well.

hep-th↗

arXiv2015

One loop partition function in AdS_3/CFT_2

The 1-loop partition function of the handle-body solutions in the AdS$_3$ gravity have been derived some years ago using the heat-kernel and the method of images. In the semiclassical limit, such partition function should correspond to the order $O (c^0)$ part in the partition function of dual conformal field theory on the boundary Riemann surface. The higher genus partition function could be computed by the multi-point functions in the Riemann sphere via sewing prescription. In the large central charge limit, to the leading order of $c$, the multi-point function is further simplified to be a summation over the product of two-point functions, which may form links. Each link is in one-to-one correspondence with the conjugacy class of the Schottky group of the Riemann surface. Moreover, the value of a link is determined by the eigenvalue of the element in the conjugate class. This allows us to reproduce exactly the gravitational 1-loop partition function. The proof can be generalized to the higher spin gravity and its dual CFT.

hep-th↗

arXiv2015

Entanglement Entropy for Descendent Local Operators in 2D CFTs

We mainly study the Rényi entropy and entanglement entropy of the states locally excited by the descendent operators in two dimensional conformal field theories (CFTs). In rational CFTs, we prove that the increase of entanglement entropy and Rényi entropy for a class of descendent operators, which are generated by $\cal{L}^{(-)}\bar{\cal{L}}^{(-)}$ onto the primary operator, always coincide with the logarithmic of quantum dimension of the corresponding primary operator. That means the Rényi entropy and entanglement entropy for these descendent operators are the same as the ones of their corresponding primary operator. For 2D rational CFTs with a boundary, we confirm that the Rényi entropy always coincides with the logarithmic of quantum dimension of the primary operator during some periods of the evolution. Furthermore, we consider more general descendent operators generated by $\sum_{} d_{\{n_i\}\{n_j\}}(\prod_{i} L_{-n_i}\prod_{j}{\bar L}_{-n_j})$ on the primary operator. For these operators, the entanglement entropy and Rényi entropy get additional corrections, as the mixing of holomorphic and anti-holomorphic Virasoro generators enhance the entanglement. Finally, we employ perturbative CFT techniques to evaluate the Rényi entropy of the excited operators in deformed CFT. The Rényi and entanglement entropies are increased, and get contributions not only from local excited operators but also from global deformation of the theory.

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