Fortschritte Der Physik

The different large limits of supersymmetric quantum field theories in three, four, and five dimensions are reviewed. The author distinguishes between the planar limit of SQCD theories, the M‐theory limit suited in three and five dimensions, and the long quiver limit. The method to solve exactly the sphere partition functions in each type of limit is spelled out in a pedagogical way. After a comprehensive general treatment of the saddle point approximation in the large limit, the author also presents an extensive list of examples and detail the calculations. The scope of this overview is to provide an entry‐level, computation‐oriented understanding of the techniques featured in the field theory side of the AdS/CFT correspondence.

Many papers on modified gravity theories (MGTs), and metric‐affine geometry have been published. New classes of black hole (BH), wormhole (WH), and cosmological solutions involving nonmetricity and torsion fields were constructed. Nevertheless, the fundamental problems of formulating nonmetric Einstein–Dirac–Maxwell (EDM), equations, and study of important nonmetric gravitational, electromagnetic and fermion effects, have not been solved in MGTs. The main goal of this work is to elaborate on a model of nonmetric EDM theory as a generalization of f(Q) gravity. The authors developed anholonomic frame and connection deformation method which allowed authors to decouple in general form and integrate nonmetric gravitational and matter fields equations. New classes of generated quasi‐stationary solutions are defined by effective sources with Dirac and Maxwell fields, nonmetricity and torsion fields, and generating functions depending, in general, on all space‐time coordinates. For respective nonholonomic parameterizations, such solutions describe nonmetric EDM deformations of BH and cosmological metrics. Variants of nonmetric BH, WH, and toroid solutions with locally anisotropic polarizations of the gravitational vacuum and masses of fermions, and effective electromagnetic sources, are constructed and analyzed. Such nonmetric deformed physical objects cannot be characterized in the framework of the Bekenstein–Hawking paradigm if certain effective horizon/holographic configurations are not involved. It is shown how to define and compute other types of nonmetric geometric thermodynamic variables using generalizations of the concept of G. Perelman W‐entropy.

The physical scalar product between spin‐networks has been shown to be a fundamental tool in the theory of topological quantum neural networks (TQNNs). These are a class of quantum neural networks supported on graphs and related to topological quantum field theory (TQFT), which have been previously introduced by the authors, recovering deep neural networks (DNNs) as their semiclassical limit. However, the effective evaluation of the scalar product remains an obstacle for the applicability of the theory. Inspired by decimation techniques for the computation of the partition function in statistical mechanics, an analytical technique is introduced for the exact evaluation of hexagonal spin‐networks of arbitrary size, and describe the corresponding algorithm for the evaluation of the physical scalar product defined by Noui and Perez. The transition amplitudes on certain classes of spin‐networks with both classical and quantum recoupling are investigated, obtaining a “continuous” spectrum of the transitions for the former and a discrete one for the latter. The theoretical and computational framework is expected to impact applications in string/tensor‐networks for solid state physics, lattice gauge theories, and quantum gravity approaches.

This paper examines the thermodynamic properties and stability of deformed AdS‐Schwarzschild black holes, focusing on the effects of deformation () and thermal correction parameters (, ) on phase transitions and heat capacity. The results show that higher values raise the Hawking‐Page critical temperature, enhancing thermal stability. Thermal corrections significantly affect smaller black holes but minimally impact larger ones, leaving second‐order phase transitions unchanged. Heat capacity analysis identifies stability regions, with sign changes marking instability. These findings highlight the role of deformation and thermal corrections in black hole stability, offering insights for extending our understanding of black hole thermodynamics.

In this paper, the authors investigate the second‐order normal quantum fluctuation on the worldsheet of a probe string in the Bañados–Teitelboim–Zanelli (BTZ) black hole. These fluctuations is treated as the projection of Hawking radiation on the worldsheet and indeed modify the action growth of the string. Then in the string field theory/boundary conformal field theory framework, via the boundary vertex operator, the authors study the correlation function of the Schrödinger functional of excited fields on the worldsheet and further extract the field's formula. This study could shed light on the potential connection between complexity growth and correlation function.

Action‐dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non‐conservative behavior, while maintaining a well‐defined notion of symmetries and a Noether theorem. This makes them especially suited for open systems. After a conceptual introduction, a quick presentation of a new mathematical framework is made for action‐dependent field theory: multicontact geometry . The formalism is illustrated with a variety of action‐dependent Lagrangians, some of which are regular and others singular, derived from well‐known theories whose Lagrangians have been modified to incorporate action‐dependent terms. Detailed computations are provided, including the constraint algorithm for the singular cases, in both the Lagrangian and Hamiltonian formalisms. These are the one‐dimensional wave equation, the Klein–Gordon equation and the telegrapher equation, Maxwell's electromagnetism, Metric‐affine gravity, the heat equation and Burgers' equation, the Bosonic string theory, and ‐dimensional gravity and Chern–Simons equation.

In this work, the behavior of interacting dark energy (DE) and dark matter (DM) within a model of gravity is explored, employing the standard framework of dynamical system analysis. The power‐law model is considered, incorporating two different forms of interacting DE and DM: and . The evolution of , , , , and for different values of the model parameter and the interaction parameter is examined. The results indicate that the universe was dominated by matter in the early stages and will be dominated by DE in later stages. The analysis shows that the fixed points are found to be stable and represent the de Sitter and quintessence acceleration solutions. It is found that the dynamical profiles of the universe in DE models are influenced by both the interaction term and the relevant model parameters.

We introduce a method that allows the Higgs to be the inflaton. The Higgs is considered as a pseudo‐Nambu‐Goldstone (pNG) boson of a global coset symmetry , which is spontaneously breaks at an energy scale . A suitable Chern−Simons (CS) interaction is given to it, with representing the dimensionless CS coupling strength and an decay constant. As a result, slow‐roll inflation occurs via ‐induced friction down a steep sinusoidal potential. To obey electroweak symmetry, the lowest‐order CS interaction is required to be quadratic in the Higgs, with the coupling strength . Higher‐order interaction terms keep the full Lagrangian nearly invariant under the approximate pNG shift symmetry. Employing the simplest symmetry coset , ‐folds of inflation occur when . Successfully explaining inflation necessitates small values of the decay constant, ; this in turn requires large , which is ruled out by electric dipole measurements. Although the electroweak hierarchy problem while achieving successful inflation, the real benefit is found in providing a different path to identifying the Higgs as the inflaton, outside the standard modified‐gravity framework.

Based on the Sen spacetime, the orbital energy and angular momentum are calculated, and the solution for the motion of a test particle derived to the second post‐Newtonian order. The effect of the Sen black hole's charge on the periastron advance and orbital period is obtained. In particular, it is found that has an influence on perihelion precession at both the first and second post‐Newtonian orders, whereas its effect on the orbital period is confined solely to the second post‐Newtonian order. Finally, the precession of the star S2 is used to constrain our model and the value of is 0.51.

The entanglement wedge duality in AdS/CFT, Karch–Randall braneworld and black hole (BH) physics is discussed, critically (as in critiques) revolving around Terashima (2024) and Mathur (2009). Emphasis are placed on the semiclassicality requirement and potential breakdown of bulk‐wise effective Hilbert space factorization between the BH exterior and the interior, supported by various examples. In particular, a simple quasi‐paradox for the entanglement wedge duality in AdS/BCFT is put forward, suggesting that it is not possible to have all of semiclassicality, the entanglement wedge duality and bulk‐wise Hilbert space factorization in Karch–Randall braneworld. Giving up factorization, a toy qudit model of BCFT is developed as to derive purification of the BH exterior, despite mostly sharing the setup with the small corrections theorem of Mathur (2009). Put together, the entanglement wedge duality is yet to be disproved despite some results by Terashima, and a toy qudit model cannot disprove semiclassicality in BH physics. The precise understanding of the duality also helps identify how the BH information paradox is dissolved within double holography beyond Karch–Randall braneworld setups.

The study of the compatibility of curvature‐matter coupling gravity theory within the framework of swampland conjectures is explored in this manuscript. The de‐sitter swampland conjecture is considered in relation to the inflationary solution generated by the curvature‐matter coupling gravity. The slow‐roll conditions are derived for the specific case of model. The results show that the swampland conjectures are at odds with the slow‐roll condition for curvature‐matter coupling gravity theory. Therefore, it is concluded that the swampland conjectures and the curvature‐matter coupling gravity, Specifically, model appear to be inconsistent with each other within the context of an inflationary profile of curvature‐matter coupling gravity theory.

A novel pathway to generate the electroweak (EW) scale via non‐perturbative dynamics of a conformally invariant scalar sector at the classical level is proposed. A method is provided to estimate the non‐perturbative EW scale generation using the exact solution of the background equations of motion in a scalar theory via the Dyson–Schwinger approach. Particularly, an analytical result for the Higgs mass in the strongly coupled regime is found in terms of its quartic self interaction term and the cut‐off scale of the theory. It is also shown that the Higgs sector is an essential part of the standard model as, without it, a Yang–Mills gauge theory cannot acquire mass even if a self‐interaction term is present. A more realistic model building with possible solutions to the gauge hierarchy problem and, in general, to the dynamical generation of any scales scales in nature, be it the visible sector or the dark sector, is led by this analysis.

The Kazakov–Solodukhin black hole (BH) metric represents a spherically symmetric deformation of the Schwarzschild solution due to quantum‐gravity corrections. Assuming the absence of nonspherical deformations of the metric, this problem was solved nonperturbatively. In this study, the intensity of Hawking radiation in the background of such quantum‐corrected BHs and the behavior of their quasinormal modes (QNM) are investigated. The findings indicate that while the geometry and such classical characteristics as the fundamental QNM frequencies or the shadow radius are only slightly altered, the Hawking radiation and the frequencies of QNM overtones of sufficiently small BHs change much more significantly. This Hawking radiation enhancement arises due to much larger grey‐body factors, while the Hawking temperature remains unaffected. The effect becomes significant at the latest stage of BH evaporation.

In this paper, the development of a spectral triple‐like construction on a configuration space of gauge connections is continued. It has previously been shown that key elements of bosonic and fermionic quantum field theory emerge from such a geometrical framework. In this paper, a central problem concerning the inclusion of fermions with half‐integer spin into this framework is solved. The tangent space of the configuration space is mapped into a similar space based on spinors, and this map is used to construct a Dirac operator on the configuration space. A real structure acting in a Hilbert space over the configuration space is also constructed. Finally, it is shown that the self‐dual and anti‐self‐dual sectors of the Hamiltonian of a nonperturbative quantum Yang‐Mills theory emerge from a unitary transformation of a Dirac equation on a configuration space of gauge fields. The dual and anti‐dual sectors are shown to emerge in a two‐by‐two matrix structure.

In this study, the features of a charged gravastar are investigated within the framework of gravity ( represents nonmetricity) using the Finch–Skea metric. This metric is applied to both the interior and shell regions of the charged gravastar and the field equations are derived accordingly. For the exterior regions, various black holes are considered, i.e., Reissner–Nordström, Bardeen, and Hayward regular black holes. The interior and exterior layers are matched using the Israel junction conditions, which help to determine the surface energy density and surface pressure for these black holes. Some physical properties such as proper length, entropy, energy, and the equation of state parameter are examined. The stability of the developed gravastar model is discussed through the effective potential, the causality condition and adiabatic index. It is concluded that the compact gravastar structure could be a viable alternative to black holes within this framework.

The simultaneous twisting of the Courant bracket by a 2‐form and a bi‐vector is investigated, with the generalized fluxes obtained in Courant algebroid relations explored. The twisted Lie bracket is defined and it is demonstrate that the generalized ‐flux can be expressed as the field strength defined on this Lie algebroid. Similarly, it is shown that the ‐flux is a direct consequence of simultaneous twisting, which arises in the twisted Lie bracket relations between holonomic partial derivatives. The generalized flux is obtained in terms of the twisted Koszul bracket, which is identified as a quasi‐Lie algebroid bracket. The action of an exterior derivative related to the twisted Koszul bracket on a bi‐vector produces the generalized ‐flux. It is shown that the generalized ‐flux is also the twisted Schouten–Nijenhuis bracket, i.e., the natural graded bracket on multi‐vectors defined with the twisted Lie bracket.

We provide a methodology for decoupling the bulk gravitational field equations of braneworld black holes to suppress the bulk singularities. Thus, we provide a regular braneworld black hole setup. To achieve this, we apply a Minimal Geometric Deformation (MGD) with respect to a coupling constant α to the 4D Minkowski spacetime embedded in an extra dimension. This results in a gravitational decoupling into a system A with equations of motion of order α 0 and a system B, related to the so-called Quasi-Einstein equations of order α. This methodology allows for the construction of a regular geometry everywhere. We outline the necessary constraints for eliminating singularities and provide a recipe for solving the equations of motion. Both the warp factor, the scalar field, and the potential obtained are smooth and free from Dirac delta singularities. A control parameter is introduced such that, in the limit b → 0, the Randall-Sundrum (RS) setup is recovered, resulting in a transition from a thick brane to a thin brane. The asymptotic behavior of the curvature invariant lim y→±∞ R 5D (r, y) is positive near the de Sitter core (for small r), asymptotically negative for finite r > r * , and asymptotically flat at the 4D boundary as r → ∞. Although this work aims to suppress bulk singularities, it is expected that our methodology may be useful for future investigations related to the embedding of gravitational objects within other braneworld contexts. a

The authors present a new method to analytically prove global stability in ghost‐ridden dynamical systems. The proposal encompasses all prior results and consequentially extends them. In particular, it is shown that stability can follow from a conserved quantity that is unbounded from below, contrary to expectation. Novel examples illustrate all of the results. The findings take root on a careful examination of the literature, here comprehensively reviewed for the first time. This work lays the mathematical basis for ulterior extensions to field theory and quantization, and it constitutes a gateway for inter‐disciplinary research in dynamics and integrability.

Symmetry Theories (SymThs) provide a flexible framework for analyzing the global categorical symmetries of a ‐dimensional in terms of a ‐dimensional bulk system . In QFTs realized via local string backgrounds, these SymThs naturally arise from dimensional reduction of the linking boundary geometry. To track possible time dependent effects we introduce a celestial generalization of the standard “boundary at infinity” of a SymTh. As an application of these considerations we revisit large quiver gauge theories realized by spacetime filling D3‐branes probing a non‐supersymmetric orbifold . Comparing the imprint of symmetry breaking on the celestial geometry at small and large ‘t Hooft coupling we find evidence for an intermediate symmetry preserving conformal fixed point.

A model is presented where a GeV axion‐like‐particle (ALP) is predicted in a large portion of the parameter space due to the presence of explicit Peccei–Quinn (PQ) symmetry‐breaking terms in an exotic leptonic sector. The latter provides a solution to the muon anomaly, within the framework of the Linear Seesaw neutrino mechanism. The spectrum is extended by a complex scalar singlet only transforming under the PQ symmetry, which generates the ALP. Its couplings with fermions can continuously span over many orders of magnitude, which constitutes a specific feature of this model in contrast to generic ultraviolet constructions. Interestingly, these couplings are suppressed by the ALP characteristic scale that can be as low as the TeV scale, which represents a novel feature of the model and opens up to several phenomenological consequences.

The integrability of two‐dimensional theories that are obtained by a dimensional reduction of certain four‐dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the presence of a potential for the neutral scalar fields is studied. For a certain solution subspace, partial integrability is demonstrated by showing that a subset of the equations of motion in two dimensions are the compatibility conditions for a linear system. Subsequently, the integrability of these two‐dimensional models is studied from a complementary one‐dimensional point of view, framed in terms of Liouville integrability. In this endeavor, various machine learning techniques are employed to systematize our search for numerical Lax pair matrices for these models, as well as conserved currents expressed as functions of phase space variables.

The Kerr metric is a vacuum solution of the Einstein equations outside of a rotating black hole (BH), but what interior matter is actually rotating and sourcing the Kerr geometry? Here, a rotating exotic matter is described, which can source the Kerr geometry for the entire acceptable range of its spin parameter and be shown to saturate the radial null‐energy condition at every point in the interior, while being free of any obvious pathologies. The rotating frozen star is introduced, whose compactness is controlled by a perturbative parameter and whose outer surface can be arbitrarily close to the horizon of a Kerr BH. The interior geometry modifies Kerr's such that there is neither an inner ergosphere nor an inner horizon. The geometry of each radial slice of the interior is a nearly null surface with the same geometry, but different radial size, as that of the would‐be horizon on the outermost slice. The integral of the energy density leads to a rest mass that is equal to the irreducible mass of a Kerr BH, and the integral of the angular‐momentum density confirms that the ratio of the angular momentum to the mass is equal to the Kerr spin parameter. Including the rotational energy in the standard way, the total gravitational mass and angular momentum of a Kerr BH with the same mass and spin parameters are obtained.

Current observations show that a significant fraction of the Universe is composed of dark energy and dark matter. In this paper, the simultaneous effects of these dark sectors on the Euler–Heisenberg black hole are investigated, using the quintessence matter field and perfect fluid to model them. In particular, the black hole's thermodynamics, shadows, and quasinormal modes are studied, and detailed discussions are provided on how these properties change with relatively large or small dark sector components.

A relation between dark energy and the scale of new physics in weakly coupled string theory is motivated. This mixing between infrared and ultraviolet physics leads to a unique corner for real‐world phenomenology: barring fine‐tunings, the authors are naturally led to the “dark dimension” scenario, a single mesoscopic extra dimension of micron size with the standard model localized on D‐branes. Our explicit top‐down worldsheet derivation establishes it on a more solid grounding. Allowing some fine‐tuning, such that the vacuum energy only arise at higher orders in string perturbation theory, the “little string theory” scenario with a very weakly coupled string is an alternative possibility. In this case, the string scale lies at the edge of detectability of particle accelerators.

The present work discusses the topic of cosmic evolution in an intriguing framework of theory of gravity (with as a non‐metricity (NM) scalar which controls the gravitational interaction) by using some recently proposed holographic dark energy (HDE) models. To achieve this goal, the dynamical equations for locally rotationally symmetric (LRS) Bianchi type‐I (BI) geometry are formulated with matter contents as a mixture of dust and anisotropic fluids. By assuming that the time‐redshift relation follows a Lambert function, the cosmological model is constructed by using Rényi HDE (RHDE), Sharma–Mittal HDE (SMHDE) and Generalized HDE (GHDE) as separate cases where Hubble horizon is taken as an infrared (IR) cutoff. Cosmological characteristics of these models are then examined through graphs of energy densities, skewness parameter , deceleration, and EoS parameters. The evolution of the EoS parameter is also studied, i.e., to discuss the dynamical characteristics of constructed DE models and assess the stability of models via the squared speed of sound parameter. It is found that the plane shows the freezing region for RHDE and GHDE models while the thawing region for the SMHDE case. Also, it is concluded that all constructed models exhibit cosmologically viable and stable behavior.