We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such couplings make the ground states close to the thermofield double states of the uncoupled Hamiltonians. For the coupled SYK model, we push the numerical computation further towards the thermodynamic limit so that an extrapolation in the size of the system is possible. We find good agreement between the extrapolated numerical result and the analytic result in the large-$q$ limit. We also consider the coupled gauged matrix model and vector model, and argue that the deconfinement is associated with the loss of the entanglement, similarly to the previous observation for the coupled SYK model. The understanding of the microscopic mechanism of the confinement/deconfinement transition enables us to estimate the quantum entanglement precisely, and backs up the dual gravity interpretation which relates the deconfinement to the disappearance of the wormhole. Our results demonstrate the importance of the entanglement between the color degrees of freedom in the emergence of the bulk geometry from quantum field theory via holography.
We study the phase transition in the holographic entanglement entropy for various confining models. This transition occurs for the entanglement entropy of a strip at a critical value of the strip width. Our main interest is to examine the critical width for models with several parameters. For these models, the critical width, the glueball mass and the string tension all become functions of these two parameters. Comparing the behavior of the critical width in the entanglement entropy and these other scales, we find that $l_c$ seems to follow closely the deconfinement temperature and the gluebal…
We study the holographic supersymmetric Yang-Mills (SYM) theory, which is living in a hyperbolic space, in terms of the entanglement entropy. The theory contains a parameter ($C$) corresponding to the excitation of the SYM theory, and it controls the dynamical properties of the theory. The entanglement temperature ($T_{ent}$) is obtained by imposing the thermodynamic law for the relative entanglement entropy and the energy density of the excitation. This temperature is available at any value of the parameter $C$ even in the region where the Hawking temperature disappears. With this new tempera…
In this paper we study the conjectural relation between confinement in a quantum field theory and the presence of a phase transition in its corresponding entanglement entropy. We determine the sufficient conditions for the latter and compare to the conditions for having a confining Wilson line. We demonstrate the relation in several examples. Superficially, it may seem that certain confining field theories with a non-local high energy behaviour, like the dual of D5 branes wrapping a two-cycle, do not admit the corresponding phase transition. However, upon closer inspection we find that, throug…
We study various entanglement measures in a one-parameter family of three-dimensional, strongly coupled Yang-Mills-Chern-Simons field theories by means of their dual supergravity descriptions. A generic field theory in this family possesses a mass gap but does not have a linear quark-antiquark potential. For the two limiting values of the parameter, the theories flow either to a fixed point or to a confining vacuum in the infrared. We show that entanglement measures are unable to discriminate confining theories from non-confining ones with a mass gap. This lends support on the idea that the ph…
We study holographic aspects of mixed state entanglement measures in various large $N$ top-down as well as bottom-up confining models. For the top-down models, we consider wrapped $D3$ and $D4$ branes gravity solutions whereas, for the bottom-up confining model, the Einstein-Maxwell-dilaton gravity solution is considered. We study entanglement entropy, mutual information, entanglement wedge cross-section and entanglement negativity for the strip subsystems and find model independent features of these entanglement measures in all confining theories. The entanglement negativity and entropy exhib…
We investigate the entanglement entropy in gravity duals of confining large $N_c$ gauge theories using the proposal of arXiv:hep-th/0603001, arXiv:hep-th/0605073. Dividing one of the directions of space into a line segment of length $l$ and its complement, the entanglement entropy between the two subspaces is given by the classical action of the minimal bulk hypersurface which approaches the endpoints of the line segment at the boundary. We find that in confining backgrounds there are generally two such surfaces. One consists of two disconnected components localized at the endpoints of the lin…
We analyze the holographic entanglement entropy in a soliton background with Wilson lines and derive a relation analogous to the first law of thermodynamics. The confinement/deconfinement phase transition occurs due to the competition of two minimal surfaces. The entropic c function probes the confinement/deconfinement phase transition. It is sensitive to the degrees of freedom (DOF) smaller than the size of a spatial circle. When the Wilson line becomes large, the entropic c function becomes non-monotonic as a function of the size and does not satisfy the usual c-theorem. We analyze the entan…
In this paper, we study the entanglement entropy between two SYK systems with bilinear coupling. We use the replica trick to calculate the entanglement entropy in the ground state. In parallel, we calculate the entanglement entropy through the Ryu-Takayanagi formula in gravity. For the ground state that is dual to an eternal traversable wormhole in AdS_2, the bulk quantum correction to the entanglement entropy is of the same order as the minimal surface area. The ground state of the coupled system is close to a thermofield double state with particular temperature and they have the same entangl…
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.
We briefly outline several main results concerning various new physically relevant features found in gravity -- both ordinary Einstein or $f(R)=R+R^2$ gravity in the first-order formalism, coupled to a special kind of nonlinear electrodynamics containing a square-root of the standard Maxwell Lagrangian and known to produce charge confinement in flat spacetime.
We demonstrate that the confinement of half-quantized vortices (HQVs) in coherently coupled Bose-Einstein condensates (BECs) simulates certain aspects of the confinement in $SU(2)$ quantum chromodynamics (QCD) in 2+1 space-time dimensions. By identifying the circulation of superfluid velocity as the baryon number and the relative phase between two components as a dual gluon, we identify HQVs in a single component as electrically charged particles with a half baryon number. Further, we show that only singlet states of the relative phase of two components can stably exist as bound states of vort…
New types of confinement phase emerge as singular SCFT's appearing as infrared-fixed-points of N=2 supersymmetric QCD (SQCD) are perturbed by an N=1 adjoint mass term. Based on a recent remarkable work on infrared-fixed-point SCFT of highest criticalities by Gaiotto, Seiberg and Tachikawa, we discuss physics of certain confining systems in SU(N), USp(2N) or SO(N) gauge theories. These show features different from a straightforward dual superconductivity picture of confinement a' la 't Hooft and Mandelstam, which might suggest a new venue in exploring the quark confinement mechanism in the real…
We consider SU(N) QCD_{1+1} coupled to massless adjoint Majorana fermions, where N is finite but arbitrary. We examine the spectrum for various values of N, paying particular attention to the formation of multi-particle states, which were recently identified by Gross, Hashimoto and Klebanov in the N -> infinity limit of the theory. It is believed that in the limit of vanishing fermion mass, there is a transition from confinement to screening in which string-like states made out of adjoint fermion bits dissociate into stable constituent ``single particles''. In this work, we provide numerical e…
We consider the soft wall model for a heuristic holographical modelling of a confining gauge theory and discuss how the introduction of a (constant) magnetic field influences the (de)confinement phase structure. We use the entanglement entropy as a diagnostic tool in terms of the length of an entangling strip geometry. Due to the anisotropy introduced by the magnetic field, we find that the results depend on the orientation of the strip relative to the field. This allows to identify a richer, anisotropic, interplay between confinement and a magnetic field than possibly can be extracted from a …
We discuss a general five-dimensional completely anisotropic holographic model with three different spatial scale factors, characterized by a Van der Waals-like phase transition between small and large black holes. A peculiar feature of the model is the relation between anisotropy of the background and anisotropy of the colliding heavy ions geometry. We calculate the holographic entanglement entropy (HEE) of the slab-shaped region, the orientation of which relatively to the beams line and the impact parameter is characterized by the Euler angles. We study the dependences of the HEE and its den…
We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form with two gauge coupling constants $e$ and $e^{\prime}$. In an axial gauge, a regularized version of the Hamiltonian of this gauge theory is $H_{0}+{e^{\prime}}^{2}H_{1}$, where $H_{0}$ is the Hamiltonian of a set of (1+1)-dimensional principal chiral nonlinear sigma models. We treat $H_{1}$ as the interaction Hamiltonian. For gauge group SU(2), we use form factors of the currents of the principal chiral sigma models to compute the string tension for small $e^{\prime}$, after reviewing exact S-matrix and form-factor me…
Confinement of excitations induces quasilocalized dynamics in disorder-free isolated quantum many-body systems in one spatial dimension. This occurrence is signalled by severe suppression of quantum correlation spreading and of entanglement growth, long-time persistence of spatial inhomogeneities, and long-lived coherent oscillations of local observables. In this work, we present a unified understanding of these dramatic effects. The slow dynamical behavior is shown to be related to the Schwinger effect in quantum electrodynamics. We demonstrate that it is quantitatively captured for long time…
The conformal affine Toda model coupled to the matter field (CATM) is obtained through a classical reduction of the $sl(2)^{(1)}$ affine two-loop WZNW model. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the so called affine Toda model coupled to the matter (ATM). Further, using a bosonization technique we recover from this theory the sine-Gordon model plus a free massless scalar field. The ATM model is considered as a QCD-motivated integrable field theory, since it describes various features in the baryonic sector of the low-e…
The main focus of this work is to test the ideas related to the oblique confinement in a theoretically controllable manner using the "deformed QCD" as a toy model. We explicitly show that the oblique confinement in the weakly coupled gauge theories emerges as a result of condensation of $N$ types of monopoles shifted by the phase $\exp(i\frac{θ+2πm}{N})$ in Bloch type construction. It should be contrasted with conventional and commonly accepted viewpoint that the confinement at $θ\neq 0$ is due to the condensation of the electrically charged dyons which indeed normally emerge in the systems wi…
The back reaction imparted by a uniform distribution of heavy static fundamental quarks on large $N_c$ strongly coupled gauge theory can be holographically realized as a deformation in $AdS$ blackhole background. The presence of back reaction brings significant changes in to the entanglement structure of the strongly coupled boundary theory at finite temperature. Since the deformed blackhole geometry still remains asymptotically $AdS$, the $gauge/gravity$ duality allows us to explore the entanglement structure of back reacted plasma in a quantitative way by computing various measures, e.g holo…
By constructing the configuration of D3-branes with D(-1)-branes as D-instantons, we study the three-dimensional Yang-Mills Chern-Simons theory in holography. Due to the presence of the D-instantons, the D7-branes with discrepant embedding functions are able to be introduced in order to include the fundamental fermions (as flavors) and the Chern-Simons term (at very low energy) in the dual theory. The vacuum structure at zero temperature is studied in the soliton background and it illustrates the topological phase transition in the presence of instantons. Moreover, since the confinement/deconf…
We consider an integrable conformally invariant two dimensional model associated to the affine Kac-Moody algebra SL(3). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing…
We develop an approach to study the entanglement in two coupled harmonic oscillators. We start by introducing an unitary transformation to end up with the solutions of the energy spectrum. These are used to construct the corresponding coherent states through the standard way. To evaluate the degree of the entanglement between the obtained states, we calculate the purity function in terms of the coherent and number states, separately. The result is yielded to two parameters dependance of the purity, which can be controlled easily. Interesting results are derived by fixing the mixing angle of su…
Quantum field theories of strongly interacting matter sometimes have a useful holographic description in terms of the variables of a gravitational theory in higher dimensions. This duality maps time dependent physics in the gauge theory to time dependent solutions of the Einstein equations in the gravity theory. In order to better understand the process by which "real world" theories such as QCD behave out of thermodynamic equilibrium, we study time dependent perturbations to states in a model of a confining, strongly coupled gauge theory via holography. Operationally, this involves solving a …
We study the vacuum structure and dyon spectrum of N=2 supersymmetric gauge theory in four dimensions, with gauge group SU(2). The theory turns out to have remarkably rich and physical properties which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and dyon masses and the metric on the moduli space of vacua. The description involves a version of Olive-Montonen electric-magnetic duality. The ``strongly coupled'' vacuum turns out to be a weakly coupled theory of monopoles, and with a suitable perturbation confinement is described by monopole co…
We consider electromagnetism in a cylindrical manifold coupled to a nonrelativistic charged point-particle. Through the relation between this theory and the Landau model on a torus, we study the entanglement between the particle and the electromagnetic field. In particular, we compute the entanglement entropy in the ground state, which is degenerate, obtaining how it varies in the degeneracy subspace.
The so-called conformal affine Toda theory coupled to the matter fields (CATM), associated to the $\hat{sl}(2)$ affine Lie algebra, is studied. The conformal symmetry is fixed by setting a connection to zero, then one defines an off-critical model, the affine Toda model coupled to the matter (ATM). The quantum version of this reduction process is discussed by means of the perturbative Lagrangian viewpoint, showing that the ATM theory is a spontaneously broken and reduced version of the CATM model. We show, using bosonization techniques that the off-critical theory decouples into a sine-Gordon …
We investigate the quantum entanglement of systems of coupled harmonic oscillators on the basis of thermo-field dynamics (TFD). For coupled harmonic oscillators at equilibrium, the extended entanglement entropy is derived using the TFD method, and it is demonstrated to be controlled by temperature and coupling parameters. For non-equilibrium systems, in addition to temperature and coupling parameters, the time dependence of the extended entanglement entropy is calculated in accordance with the dissipative von Neumann equation, and the dissipative dynamics of the systems of coupled harmonic osc…
The entanglement of the coupled massive scalar field in the spacetime of a Garfinkle-Horowitz-Strominger(GHS) dilaton black hole has been investigated. It is found that the entanglement does not depend on the mass of the particle and the coupling between the scalar field and the gravitational field, but it decreases as the dilaton parameter $D$ increases. It is interesting to note that in the limit of $D\to M$, corresponding to the case of an extreme black hole, the state has no longer distillable entanglement for any state parameter $α$, but the mutual information equals to a nonvanishing min…
We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in the Minkowski vacuum, and in the Born-Markov approximation the master equation that describes the completely positive time evolution of the two-atom system is derived. In particular, we investigate the phenomena of entanglement degradation, generation, revival and enhancement. As opposed to the scalar-field case, the entanglement dynamics is crucially dependen…
