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 line segment. The other contains a tube connecting the two components. The disconnected surface dominates the entropy for $l$ above a certain critical value $l_{\rm crit}$ while the connected one dominates below that value. The change of behavior at $l=l_{\rm crit}$ is reminiscent of the finite temperature deconfinement transition: for $l < l_{\rm crit}$ the entropy scales as $N_c^2$, while for $l > l_{\rm crit}$ as $N_c^0$. We argue that a similar transition should occur in any field theory with a Hagedorn spectrum of non-interacting bound states. The requirement that the entanglement entropy has a phase transition may be useful in constraining gravity duals of confining theories.
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…
The mechanism of color confinement as a consequence of an unbroken non-abelian gauge symmetry and asymptotic freedom is elucidated and compared with that of other models based on an analogy with the type II superconductor. It is demonstrated that a sufficient condition for color confinement is given by $Z_3^{-1}=0$ where $Z_3$ denotes the renormalization constant of the color gauge field. It is shown that this condition is actually satisfied in quantum chromodynamics and that some of the characteristic features of other models follow from it.
We review classical results on holographic entanglement entropy utilizing the Hamilton-Jacobi approach. Possibility of using the entanglement entropy as a probe of confinement is shortly discussed in the context of lattice data.
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…
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…
The notion of generalized gravitational entropy introduced by Lewkowycz and Maldacena allows, via the AdS/CFT correspondence, to calculate CFT entanglement entropies. We adapt the method to the case where flavor branes are present and treated in the probe approximation. This allows to calculate the leading flavor correction to the CFT entanglement entropy from the on-shell action of the probe, while dealing with the backreaction is avoided entirely and from the outset. As an application we give concise derivations for the contribution of massless and massive flavor degrees of freedom to the en…
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 compute the holographic entanglement entropy contribution from planar two-dimensional defects in six-dimensional $\mathcal{N}=(2,0)$ superconformal field theory, holographically dual to probe M2- and M5-branes in $AdS_7 \times S^4$. In particular, we test the viability of the universal contribution of the defect to entanglement entropy as a candidate $C$-function. We find that this coefficient is not monotonic under defect renormalization group flows triggered by the vacuum expectation value of a marginal operator. Another candidate $C$-function, the on-shell action inside the entanglement …
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…
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.
In the context of Matrix/light-cone gauge M-theory, we develop a new approach for computing quantum entanglement between a probe gravitating in the vicinity of a source mass and the source mass. We demonstrate that this entanglement is related to the gravitational potential energy between the two objects. We then show that the Von Neumann entropy is a function of two derivatives of the gravitational potential. We conjecture a relation between the entropy and the local Riemann tensor sampled by the probe, establishing a general scheme to relate entropy to local geometric data. This relation con…
Multipartite Entanglement Can Probe Wormhole Moduli Invisible to Bipartite Entanglement
Yonago College, National Institute of Technology（米子工业高等专门学校）；National Tsing Hua University（国立清华大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Using Matrix theory, we propose a technique on how to compute the entangle- ment entropy between a supergravity probe and modes on a spherical membrane. We demonstrate that a membrane stretched between the probe and the sphere entangles these modes and can lead to an the entanglement entropy that encodes information about local gravitational geometry seen by the probe.
We study holographic entanglement entropy in Gauss-Bonnet gravity following a global quench. It is known that in dynamical scenarios the entanglement entropy probe penetrates the apparent horizon. The goal of this work is to study how far behind the horizon can the entanglement probe reach in a Gauss-Bonnet theory. We find that the behavior is quite different depending on the sign of the Gauss-Bonnet coupling $λ_{GB}$. We show that for $λ_{GB} > 0$ the holographic entanglement entropy probe explores less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for $λ_{G…
From the viewpoint of holography, we study the behaviors of the entanglement entropy in insulator/superconductor transition with exponential nonlinear electrodynamics (ENE). We find that the entanglement entropy is a good probe to the properties of the holographic phase transition. Both in the half space and the belt space, the non-monotonic behavior of the entanglement entropy in superconducting phase versus the chemical potential is general in this model. Furthermore, the behavior of the entanglement entropy for the strip geometry shows that the confinement/deconfinement phase transition app…
In this paper we investigate the relation between the bulk and boundary in AdS/CFT. We first discuss the relation between the Poincare and the global vacua, and then study various probes of the bulk from the boundary theory point of view. We derive expressions for retarded propagators and note that objects in free fall look like expanding bubbles in the boundary theory. We also study several Yang-Mills theory examples where we investigate thermal screening and confinement using propagators. In the case of confinement we also calculate the profile of a flux tube and provide an alternative deriv…
In this Letter we use the Julia-Toulouse approach for condensation of defects in order to obtain an effective confinement theory for external chromoelectric probe charges in SU(3) gauge theory in the regime with condensed chromomagnetic monopoles. We use the Cho decomposition of the non-Abelian connection in order to reveal the Abelian sector of the non-Abelian gauge theory and the associated topological defects (monopoles) without resorting to any gauge fixing procedure. Using only the Abelian sector of the theory, we construct a hydrodynamic effective theory for the regime with condensed def…
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 give a prescription for calculating the entanglement entropy in holographic probe brane systems by systematically taking the leading order backreaction of the probe brane into account. We find a simple compact double integral formula, which is insensitive to many details of the backreaction, most notably the internal space or the non-metric fields sourced by the probe. We validate our method by comparing to exact results in solvable toy models. We also determine the entanglement entropies for a sphere and a strip in the top-down D3/D7 and D3/D5 system. For the sphere the entanglement entrop…
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…
In the setting of the Berenstein-Maldacena-Nastase Matrix theory, dual to light-cone M-theory in a PP-wave background, we compute the Von Neumann entanglement entropy between a probe giant graviton and a source. We demonstrate that this entanglement entropy is directly and generally related to the local tidal acceleration experienced by the probe. This establishes a new map between local spacetime geometry and quantum entanglement, suggesting a mechanism through which geometry emerges from Matrix quantum mechanics. We extend this setting to light-cone M-theory in flat space, or the Banks-Fisch…
We study the entanglement entropy as a probe of the proximity effect of a superconducting system by using the gauge/gravity duality in a fully back-reacted gravity system. While the entanglement entropy in the superconducting phase is less than the entanglement entropy in the normal phase, we find that near the contact interface of the superconducting to normal phase the entanglement entropy has a different behavior due to the leakage of Cooper pairs to the normal phase. We verify this behavior by calculating the conductivity near the boundary interface.
Topological entanglement entropy, a measure of the long-ranged entanglement, is related to the degeneracy of the ground state on a higher genus surface. The exact relation depends on the details of the topological theory. We consider a class of holographic models where such relation might be similar to the one exhibited by Chern-Simons theory in a certain large N limit. Both the non-vanishing topological entanglement entropy and the ground state degeneracy in these holographic models are consequences of the topological Gauss-Bonnet term in the dual gravitational description. A soft wall hologr…
A holographic bottom-up model used in studying the superconducting system is applied to search for the color superconducting phase of supersymmetric Yang-Mills theory. We apply the probe analysis of this model to the supersymmetric Yang-Mills theory in both the confinement and deconfinement phases. In this analysis, we find the color superconductivity in both phases when the baryon chemical potential exceeds a certain critical value. This result implies that, above the critical chemical potential, a color non-singlet diquark operator, namely the Cooper pair, has its vacuum expectation value ev…
We study the behaviors of entanglement entropy and vacuum expectation value of Wilson loop in the Stückelberg holographic insulator/superconductor model. This model has rich phase structures depending on model parameters. Both the entanglement entropy for a strip geometry and the heavy quark potential from the Wilson loop show that there exists a "confinement/deconfinement" phase transition. In addition, we find that the non-monotonic behavior of the entanglement entropy with respect to chemical potential is universal in this model. The pseudo potential from the spatial Wilson loop also has a …
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 …
In this paper, we study the generic action for the scale-invariant theory of gravity and then by making use of the holographic methods, we compute some specific holographic measures of entanglement. Precisely, we calculate the entanglement entropy, mutual and tripartite information and show that the mutual information is always positive while the tripartite information becomes negative. This indeed recovers the monogamy property of mutual information in this context.
Confinement and chiral symmetry breaking in holography: a smooth switch-off
Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Instituto Galego de Física de Altas Enerxías (IGFAE)（加利西亚高能物理研究所）；Julius Maximilians University Würzburg（维尔茨堡朱利叶斯·马克西米利安大学）；University of Southampton（南安普顿大学）
We show that, in 1+1 dimensional gauge theories, a heavy probe charge is screened by dynamical massless fermions both in the case when the source and the dynamical fermions belong to the same representation of the gauge group and, unexpectedly, in the case when the representation of the probe charge is smaller than the representation of the massless fermions. Thus, a fractionally charged heavy probe is screened by dynamical fermions of integer charge in the massless Schwinger model, and a colored probe in the fundamental representation is screened in $QCD_2$ with adjoint massless Majorana ferm…
Based on gauge-gravity duality, by using holographic entanglement entropy, we have done a phenomenological study to probe confinement-deconfinement phase transition in the QCD-like gauge theory. Our outcomes are in perfect agreement with the expected results, qualitatively and quantitatively. We find out that the (holographic) entanglement entropy is a reliable order parameter for probing the phase transition.
In this paper, we investigate the holographic phase transition with dark matter sector in the AdS black hole background away from the probe limit. We disclose the properties of phases mostly from the holographic topological entanglement entropy of the system. We find the entanglement entropy is a good probe to the critical temperature and the order of the phase transition in the general model. The behaviors of entanglement entropy at large strip size suggest that the area law still holds with dark matter sector. We also conclude that the holographic topological entanglement entropy is useful i…
We investigate the behavior of the entanglement entropy of a confining gauge theory near cosmological singularities using gauge/gravity duality. As expected, the coefficients of the UV divergent terms are given by simple geometric properties of the entangling surface in the time-dependent background. The finite (universal) part of the entanglement entropy either grows without bound or remains bounded depending on the nature of the singularity and entangling region. We also discuss a confinement/deconfinement phase transition as signaled by the entanglement entropy.
We investigate the behaviors of holographic entanglement entropy for AdS soliton geometries in the presence of higher derivative corrections. We calculate the leading higher derivative corrections for the AdS5 setup in type IIB string and for the AdS4,7 ones in M-theory. We also study the holographic entanglement entropy in Gauss-Bonnet gravity and study how the confinement/deconfinement phase transition observed in AdS solitons is affected by the higher derivative corrections.
We explore the entanglement of the vacuum of a relativistic field by letting a pair of causally disconnected probes interact with the field. We find that, even when the probes are initially non-entangled, they can wind up to a final entangled state. This shows that entanglement persists between disconnected regions in the vacuum. However the probe entanglement, unlike correlations, vanishes once the regions become sufficiently separated. The relation between entropy, correlations and entanglement is discussed.
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…
We study the short-distance structure of geometric entanglement entropy in certain theories with a built-in scale of nonlocality. In particular we examine the cases of Little String Theory and Noncommutative Yang-Mills theory, using their AdS/CFT descriptions. We compute the entanglement entropy via the holographic ansatz of Ryu and Takayanagi to conclude that the area law is violated at distance scales that sample the nonlocality of these models, being replaced by an extensive volume law. In the case of the noncommutative model, the critical length scale that reveals the area/volume law trans…
Vacuum entanglement probes for ultra-cold atom systems
School of Mathematical Sciences, University of Nottingham（诺丁汉大学数学科学学院）；University of Nottingham（诺丁汉大学）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文学系）；University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham（诺丁汉大学量子非平衡系统数学与理论物理中心）
In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.
We propose a covariant prescription to compute holographic entanglement entropy and Poincare blocks (Global BMS blocks) in the context of three-dimensional Einstein gravity in flat space. We first present a prescription based on worldline methods in the probe limit, inspired by recent analog calculations in AdS/CFT. Building on this construction, we propose a full extrapolate dictionary and use it to compute holographic correlators and blocks away from the probe limit.
We investigate the behavior of entanglement entropy in the holographic QCD model proposed by Gubser et al. By choosing suitable parameters of the scalar self-interaction potential, this model can exhibit various types of phase structures: crossover, first order and second order phase transitions. We use entanglement entropy to probe the crossover/phase transition, and find that it drops quickly/suddenly when the temperature approaches the critical point which can be seen as a signal of confinement. Moreover, the critical behavior of the entanglement entropy suggests that we may use it to chara…
In this paper, we study the Lorentzian AdS wormhole solutions constructed in arXiv:0808.2481 [hep-th]. Each of them is a classical solution interpolating between an AdS space and a flat space in type IIB supergravity. We calculate the holographic entanglement entropy to probe this geometry. Our analysis shows that there exits a mass gap in its holographic dual gauge theory and that the entanglement between the two boundaries is rather suppressed than that we naively expect for wormholes. We also examine the holographic conductivity on a probe D-brane in this spacetime.
Using non-linear evolution equations of QCD, we compute the von Neumann entropy of the system of partons resolved by deep inelastic scattering at a given Bjorken $x$ and momentum transfer $q^2 = - Q^2$. We interpret the result as the entropy of entanglement between the spatial region probed by deep inelastic scattering and the rest of the proton. At small $x$ the relation between the entanglement entropy $S(x)$ and the parton distribution $xG(x)$ becomes very simple: $S(x) = \ln[ xG(x) ]$. In this small $x$, large rapidity $Y$ regime, all partonic micro-states have equal probabilities -- the p…
