Search Results (33)

The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. These can be regarded as specific probabilistic models for tensors with particular geometry dictated by a graph (or network) structure. First, we introduce a model of RTN obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). The entanglement spectrum of the resulting random state is analyzed along a given bipartition of the local Hilbert spaces. The limiting eigenvalue distribution of the reduced density operator of the RTN state is provided in the limit of large local dimension. This limiting value is described through a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, an explicit formula for the limiting eigenvalue distribution is provided using classical and free multiplicative convolutions. The physical implications of these results are discussed, allowing the analysis to move beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN. Full article

As shown by Dyson in his famous paper “Missed Opportunities”, it follows, even from purely mathematical considerations, that quantum Poincare symmetry is a special degenerate case of quantum de Sitter symmetries. Thus, the usual explanation of why, in particle physics, Poincare symmetry works with a very high accuracy is as follows. A theory in de Sitter space becomes a theory in Minkowski space when the radius of de Sitter space is very high. However, the answer to this question must be given only in terms of quantum concepts, while de Sitter and Minkowski spaces are purely classical concepts. Quantum Poincare symmetry is a good approximate symmetry if the eigenvalues of the representation operators $M_{4\mu }$ of the anti-de Sitter algebra are much greater than the eigenvalues of the operators $M_{\mu \nu }$ ($\mu ,\nu =0,1,2,3$). We explicitly show that this is the case in the Flato–Fronsdal approach, where elementary particles in standard theory are bound states of two Dirac singletons. Full article

In this work, we obtained exact solutions of Einstein’s field equations for plane symmetric cosmological models by assuming that they admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum and conformally flat. We have shown that in the case of a perfect fluid, these solutions have an energy-momentum tensor possessing dark energy with negative pressure and the energy equation of state is $\rho +p=0$. We have shown that a fluid has acceleration, rotation, shear-free, vanishing expansion, and rotation. In the case of a cosmic string cloud, we found that the tension density and particle density decrease as the fluid moves along the direction of the strings, then vanish at infinity. We shown that the exact conformal solution for a static plane symmetric model reduces to the well-known anti-De Sitter space-time. We obtained that the space-time under consideration admits a conformal vector field orthogonal to the 4-velocity vector and does not admits a vector parallel to the 4-velocity vector. Some physical and kinematic properties of the resulting models are also discussed. Full article

Particular Kottler spacetimes are analytically investigated. The investigated spacetimes are spherically symmetric nonrotating spacetimes endowed with a Schwarzschild solid-angle element. SchwarzschildNairiai spacetimes, Schwarzschild spacetimes with a linear term, and Schwarzschild spacetimes with a linear term and a cosmological constant are studied. The infinite-redshift surfaces are analytically written. To this aim, the parameter spaces of the models are analytically investigated, and the conditions for which the analytical radii are reconducted to the physical horizons are used to set and to constrain the parameter spaces. The coordinate-singularity-avoiding coordinate extensions are newly written. Schwarzschild spacetimes with a linear term and a cosmological constant termare analytically studied, and the new singularity-avoiding coordinate extensions are detailed. The new roles of the linear term and of the cosmological constant term in characterizing the Schwarzschild radius are traced. The generalized Schwarzschild–deSitter case and generalized Schwarzschild–anti-deSitter case are characterized in a different manner. The weak field limit is newly recalled. The embeddings are newly provided. The quantum implementation is newly envisaged. The geometrical objects are newly calculated. As a result, for the Einstein field equations, the presence of quintessence is newly excluded. The Birkhoff theorem is newly proven to be obeyed. Full article

We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in an extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We prove the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and the phase transitions are studied. It is shown that the electric fields of charged objects at the origin and the electrostatic self-energy are finite within the nonlinear electrodynamics proposed. Full article

The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential. Full article

We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group—subject to a Young tableaux $Y(s_1,\dots ,s_k)$ with $k\ge 2$ rows—in a d-dimensional anti-de Sitter space. Auxiliary representations for a deformed non-linear HS symmetry algebra in terms of a generalized Verma module, as applied to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints, are found explicitly in the case of a $k=2$ Young tableaux. An oscillator realization over the Heisenberg algebra for the Verma module is constructed. The results generalize the method of constructing auxiliary representations for the symplectic $sp\left(2k\right)$ algebra used for mixed-symmetry HS fields in flat spaces [Buchbinder, I.L.; et al. Nucl. Phys. B 2012, 862, 270–326]. Polynomial deformations of the $su(1,1)$ algebra related to the Bethe ansatz are studied as a byproduct. A nilpotent BRST operator for a non-linear HS symmetry algebra of the converted constraints for $Y(s_1,s_2)$ is found, with non-vanishing terms (resolving the Jacobi identities) of the third order in powers of ghost coordinates. A gauge-invariant unconstrained reducible Lagrangian formulation for a free bosonic HS field of generalized spin $(s_1,s_2)$ is deduced. Following the results of [Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470.; Buchbinder, I.L.; et al. arXiv 2022, arXiv:2212.07097], we develop a BRST approach to constructing general off-shell local cubic interaction vertices for irreducible massive higher-spin fields (being candidates for massive particles in the Dark Matter problem). A new reducible gauge-invariant Lagrangian formulation for an antisymmetric massive tensor field of spin $(1,1)$ is obtained. Full article

The Reissner–Nordstrom spacetimes and some generalised Reissner–Nordstrom spacetimes are analysed. The blackhole solutions are considered. The generalised Reissner–Nordstrom spacetimes with a cosmological-constant term, endowed with a Schwarzschild solid-angle element, are analytically delineated: the radii of the blackholes are analytically calculated and newly parameterised; the coordinate-singularity-avoiding coordinate extension is newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the new conditions for merging the solutions as the physical horizons are analytically outlined; the new parameter space of the model is set and constrained; the new role of the cosmological-constant term in designating the Schwarzschild radius is demonstrated; the Reissner–Nordstrom–deSitter case and in the Reissner–Nordstrom–anti-deSitter one are newly demonstrated to be characterised in a different analytical manner. Furthermore, a new family of solutions is found, qualified after the cosmological-constant term. The generalised Reissner–Nordstrom spacetimes with a linear term, endowed with a Schwarzschild solid-angle element, are analytically studied: the radii are enumerated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are set; the new parameter space of the system is arranged and constrained; the role of the linear-term parameter in the delineation of the Schwarzschild radius is newly proven to be apt to imply a small modification only. The generalised Reissner–Nordstrom spacetimes, endowed with a Schwarzschild solid-angle element, with a linear term and a cosmological-constant term are newly inspected: the radii are analytically calculated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are prescribed; the new parameter space of the scheme is appointed and constrained; the roles of the parameters are newly scrutinised in their application to modify the physical interpretation of the Reissner–Nordstrom parameters only in a small manner; the coordinate-singularity-avoiding coordinate extensions are newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the definition of the physical radii is newly found; the results are newly demonstrated in both cases of a positive value of the cosmological constant and in the case of a negative value of the cosmological constant in a different manner; the role of the linear-term parameter is also newly enunciated. More over, a new family of solutions is found, which is delineated after particular values of the linear term and of the cosmological-constant one. The quantum implementation of the models is prospectively envisaged. Full article

The Hawking temperature for a Schwarzschild black hole is $T=1/8\pi M$, where M is the black hole mass. This formula is derived for a fixed Schwarzschild background metric, where the mass M could be arbitrary small. Note that, for vanishing $M\to 0$, the temperature T becomes infinite. However, the Schwarzschild metric itself is regular when the black hole mass M tends to zero; it is reduced to the Minkowski metric, and there are no reasons to believe that the temperature becomes infinite. We point out that this discrepancy may be due to the fact that the Kruskal coordinates are singular in the limit of the vanishing mass of the black hole. To elucidate the situation, new coordinates for the Schwarzschild metric are introduced, called thermal coordinates, which depend on the black hole mass M and the parameter b. The parameter b specifies the motion of the observer along a special trajectory. The thermal coordinates are regular in the limit of vanishing black hole mass M. In this limit, the Schwarzschild metric is reduced to the Minkowski metric, written in coordinates dual to the Rindler coordinates. Using the thermal coordinates, the Schwarzschild black hole radiation is reconsidered, and it is found that the Hawking formula for temperature is valid only for large black holes, while for small black holes, the temperature is $T=1/2\pi (4M+b)$. The thermal observer in Minkowski space sees radiation with temperature $T=1/2\pi b$, similar to the Unruh effect with non-constant acceleration. The thermal coordinates for more general spherically symmetric metrics, including the Reissner–Nordstrom, de Sitter, and anti-de Sitter, are also considered. In these coordinates, one sees a Planck distribution with constant temperature. One obtains that the thermal Planck distribution of massless particles is not restricted to the cases of black holes or constant acceleration, but is valid for any spherically symmetric metric written in thermal coordinates. Full article

The thermodynamics and phase transitions of magnetic Anti-de Sitter black holes were studied. We considered extended-phase-space thermodynamics, with the cosmological constant being a thermodynamic pressure and the black hole mass being treated as a chemical enthalpy. The extended-phase-space thermodynamics of black holes mimic the behavior of a Van der Waals liquid. Quantities conjugated to the coupling of nonlinear electrodynamics (NED) and a magnetic charge are obtained. Thermodynamic critical points of phase transitions are investigated. It was demonstrated that the first law of black hole thermodynamics and the generalized Smarr relation hold. The Joule–Thomson adiabatic expansion of NED-AdS black holes is studied. The dependence of inversion temperature on pressure and the minimum of the inversion temperature are found. Full article

We consider maximal gauged supergravity in 4D with the $\mathrm{ISO}\left(7\right)$ gauge group, which arises from a consistent truncation of massive IIA supergravity on a six-sphere. Within its G${}_2$-invariant sector, the theory is known to possess a supersymmetric AdS extremum, as well as two non-supersymmetric ones. In this context, we provide a first-order formulation of the theory by making use of the Hamilton–Jacobi (HJ) formalism. This allows us to derive a positive energy theorem for both non-supersymmetric extrema. Subsequently, we also find novel non-supersymmetric domain walls (DWs) interpolating between the supersymmetric extremum and each of the other two. Finally, we discuss a perturbative HJ technique that may be used in order to solve for curved DW geometries. Full article

In this paper, we analyzed the fermionic condensate (FC) associated with a massive fermionic field on a five-dimensional anti-de Sitter (AdS) spacetime in the presence of a cosmic string taking into account a magnetic flux running along its core. In addition, a compactified dimension was considered. Due to this compactification, the FC is expressed in terms of two distinct contributions: the first one corresponds to the geometry without compactification, and the second one is induced by the compactification. Depending on the values of the physical parameters, the total FC can be positive or negative. As a limiting case, the expression for the FC on locally Minkowski spacetime was derived. It vanishes for a massless fermionic field, and the nonzero FC on the AdS background space in the massless case is an effect induced by gravitation. This shows that the gravitational field may essentially influence the parameter space for phase transitions. For a massive field, the FC diverges on the string as the inverse cube of the proper distance from the string. In the case of a massless field, depending on the magnetic flux along the string and planar angle deficit, the limiting value of the FC on the string can be either finite or infinite. At large distances, the decay of the FC as a function of the distance from the string is a power law for both cases of massive and massless fields. For a cosmic string on the Minkowski bulk and for a massive field, the decay is exponential. The topological part in the FC vanishes on the AdS boundary. We show that the FCs coincide for the fields realizing two inequivalent irreducible representations of the Clifford algebra. In the special case of the zero planar angle deficit, the results presented in this paper describe Aharonov–Bohm-type effects induced by magnetic fluxes in curved spacetime. Full article

Quantum neurobiology is concerned with potential quantum effects operating in the brain and the application of quantum information science to neuroscience problems, the latter of which is the main focus of the current paper. The human brain is fundamentally a multiscalar problem, with complex behavior spanning nine orders of magnitude-scale tiers from the atomic and cellular level to brain networks and the central nervous system. In this review, we discuss a new generation of bio-inspired quantum technologies in the emerging field of quantum neurobiology and present a novel physics-inspired theory of neural signaling (AdS/Brain (anti-de Sitter space)). Three tiers of quantum information science-directed neurobiology applications can be identified. First are those that interpret empirical data from neural imaging modalities (EEG, MRI, CT, PET scans), protein folding, and genomics with wavefunctions and quantum machine learning. Second are those that develop neural dynamics as a broad approach to quantum neurobiology, consisting of superpositioned data modeling evaluated with quantum probability, neural field theories, filamentary signaling, and quantum nanoscience. Third is neuroscience physics interpretations of foundational physics findings in the context of neurobiology. The benefit of this work is the possibility of an improved understanding of the resolution of neuropathologies such as Alzheimer’s disease. Full article

Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space of an unconfined ideal gas in an anti-de Sitter background. Notwithstanding the gas’ freedom to move in an infinite volume, we establish necessary conditions for the stationary probability distribution solving a general maximum entropy problem to be normalizable and obtain the resulting probability for a particular choice of constraints. As a part of our analysis, we develop a novel method for identifying dynamical constraints based on local measurements. With no appeal to a priori information about globally defined conserved quantities, it is therefore applicable to a much wider range of problems. Full article

In the same way as the realization of some of the famous gedanken experiments imagined by the founding fathers of quantum mechanics has recently led to the current renewal of the interpretation of quantum physics, it seems that the most recent progress of observational astrophysics can be interpreted as the realization of some cosmological gedanken experiments such as the removal from the universe of the whole visible matter or the cosmic time travel leading to a new cosmological standard model. This standard model involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the cosmological constant, we propose explaining dark matter as a pure QCD effect, namely a gluonic Bose–Einstein condensate, following the transition from the quark gluon plasma phase to the colorless hadronic phase. Our approach not only allows us to assume a Dark/Visible ratio equal to 11/2 but also provides gluons (and di-gluons, viewed as quasi-particles) with an extra mass of vibrational nature. Such an interpretation would support the idea that, apart from the violation of the matter/antimatter symmetry satisfying the Sakharov’s conditions, the reconciliation of particle physics and cosmology needs not the recourse to any ad hoc fields, particles or hidden variables. Full article