In the standard formulation of relativistic quantum field theory, a Z2-graded structure is assumed to realize locality and the boson–fermion dichotomy. While Z2n-graded extensions are known to be allowed at the level of symmetry, their realization in interacting quantum field theories remains unclear.In this paper, we construct a minimal Z22-graded classical supersymmetric Yang–Mills theory. We derive the invariant action and show that all kinetic terms have the standard sign, indicating the absence of classical ghost-like instabilities. Moreover, the positivity of the Hamiltonian follows from the Z22-graded supersymmetry algebra. We thus show that Z22-graded generalized statistics can be realized at the classical level in a stable interacting supersymmetric gauge theory.
We investigate the Wilson line sector contribution to holographic complexity for five-dimensional Einstein-Gauss-Bonnet AdS black holes immersed in a static string cloud, working within the complexity equals action framework. The string cloud induces geometric backreaction on the AdS background, while the Gauss-Bonnet (GB) term captures higher derivative curvature corrections from string theory. Following the probe string formalism established in previous works, we compute the time growth rate of the Nambu-Goto worldsheet action for a moving fundamental string over a range of probe velocities, string cloud densities, and GB coupling strengths. This observable isolates nonlocal contributions from heavy Wilson line operators in the dual boundary theory, rather than evaluating the full gravitational action on the Wheeler-DeWitt patch. Our numerical results reveal a nontrivial competition between spacetime backreaction and curvature corrections, governed primarily by the black hole horizon size and probe kinematics. For large black holes, increasing the string cloud density accelerates the Wilson line complexity growth for slowly moving probes but suppresses it at relativistic velocities, producing a characteristic velocity dependent crossover. Small black holes exhibit no such crossover, with complexity rising monotonically with cloud density for all probe speeds. GB curvature corrections reduce the probe string complexity growth across all parameter choices, with much stronger suppression acting on small black holes due to their enhanced near horizon curvature. Beyond critical values of the GB coupling and cloud density, thermodynamically unstable small black hole solutions disappear, and the single surviving stable black hole recovers the dynamical signatures of large black hole geometries. Geometric analysis shows that slowly moving strings access deeper bulk regions and amplify complexity, while relativistic probes remain confined near the horizon and yield lower complexity growth. This work demonstrates that the horizon scale controls the interplay between background geometric deformations and the Wilson line sector of holographic complexity in strongly coupled conformal theories.
In this paper, we construct a holographic antiferromagnetism model by introducing two real antisymmetric tensor fields that are coupled to the background gauge field strength and interact with each other within a four-dimensional Gauss-Bonnet gravity background, and investigate the influence of the Gauss-Bonnet coupling constant c on the paramagnetism-antiferromagnetism phase transition. Through numerical shooting method, we discover that a phase transition exists in Gauss-Bonnet black hole under the probe limit. In the absence of an external magnetic field, the increase of value c raises the critical temperature, making the paramagnetism-antiferromagnetism phase transition more likely to occur. When an external magnetic field is present, the magnetic susceptibility follows the Curie-Weiss law with temperature in the paramagnetic phase region, exhibiting a pronounced peak at the critical temperature. Furthermore, the peak value of the susceptibility increases with the increasing of c.
We study the phase structure of a backreacted Einstein–Maxwell holographic superconductor with a gauge-invariant quartic scalar self-interaction V(ψ)=m2|ψ|2+λ|ψ|4 in (3+1)-dimensional asymptotically AdS spacetime. The reduced equations of motion are derived from the action by symbolic tensor calculus and validated against the exact Reissner–Nordström–AdS4 solution to better than one part in 106. At κ2=1, λ˜=0.1, standard quantization, a scan over seventeen charges q ∈ [1.0, 4.0] shows second-order-like behavior for q ≲ 1.8 and q ≳ 3.3, and a first-order window in between, confirmed by exact thermodynamic integration of the free energy and by a positive latent heat at two representative points (ℓ/μ3 ≃ 0.106 and 0.277), bounded by two tricritical points located at qtrilower=1.79±0.01 and qtriupper=3.28±0.01 (bisection resolution). This two-tricritical-point structure differs from the single-TCP phase diagram previously reported for this model and persists at a second coupling, λ˜=0.05. A numerical fit of the order-parameter critical exponent on an ordinary second-order line gives β=0.25–0.40 depending on the fitting window, not yet resolving between the mean-field value 1/2 and the tricritical value 1/4 at the precision and proximity to Tc accessible with the present solver. We derive the coupled gauge-field/metric-perturbation equations governing the optical conductivity; a first-order constraint from the linearized Einstein zx equation reduces the associated shooting problem to a single complex parameter, which we solve numerically and validate against the known normal-phase asymptotic conductivity, |σ(ω → ∞)| → 1 to four decimal places. A representative superconducting-phase point does not show a resolved spectral gap within the frequency range explored, and the zero-frequency spectral weight is comparable in magnitude to its normal-phase, momentum-conservation counterpart, so it cannot be attributed to superfluid density without a momentum-relaxation deformation not implemented here. A holographic entanglement-entropy calculation for a boundary strip is implemented, validated against the expected universal UV divergence, and restricted to the thermodynamically stable branch. We do not find, and do not claim, topological superconductivity in the sense of a bulk topological invariant, protected edge state, or Majorana mode.
This paper provides the analysis of relativistic compact star models in the context of general relativity with the addition of the dark matter (DM) effect in the form of the Burkert profile. Since DM could potentially influence the dynamics of galaxies, as well as the internal structure of compact astrophysical objects, we consider four famous neutron stars (PSR J0740+6620, PSR J0348+0432, PSR J1614-2230, and 4U 1724-207) using their observed masses together with representative radii as a physical constraint and discuss the effect of DM on the characteristic features of these star models. This adopted density profile acts as an effective matter density distribution for the construction of regular compact star configurations and is not meant to be treated as a realistic two-fluid DM admixed system. We set one metric potential and find the other based on a highly motivated DM density profile, in a spherically symmetric, static spacetime. This provides a consistent solution to the Einstein field equations. These configurations are scrutinized through essential physical metrics, the effective equation of state, energy conditions, conservation equation, adiabatic index, active gravitational mass, compactness, and redshift to evaluate physical viability and feasibility. The results are compatible with observational constraints and suitable parametric choices and show that DM clearly modifies the interior structure of compact stars, especially in the pressure evolution and gravitational characteristics. In summary, this work explores the influence of a Burkert-inspired cored matter distribution on the geometric and physical properties of compact stellar configurations.
In [1], inspired by the works [7–30], a prescription for calculating the correlation functions in Quadratic Gravity [31-32] was presented and further exploited in [2–5]. A covariant formalism ensuring positive definite probabilities is worked out, which is the main drawback of Quadratic Gravity. The Gauss-Ostrogradsky method for Quadratic Gravity defines two momentum densities P1 and P2 and two coordinate densities Q1 and Q2, one pair is standard, the other ghost like. The approach in [1] involves the continuation P2 → iP2 and Q2 → iQ2 of the ghost variables acting on kets | > after taking mean values. The notable result is that, in the euclidean setting, this procedure leads to Quadratic Gravity path integral Z(J), thus renormalizability is not spoiled. In view of these findings, it is natural to ask how the LSZ rules of the model have to be formulated, and this is the topic of the present work. A formalism adapted to full quartic or higher order theories is worked out, extending the results of [39]. The main technical point is to determine the creation annihilation algebra for the graviton modes, adapted to the present prescription, and properly dealing with gauge symmetry. This makes the problem harder than the quantization of the Pais-Uhlenbeck model. Two possible quantization schemes are discussed, they depend on whether the above prescriptions are applied at the beginning or at the end of the LSZ calculation.
Black-hole thermodynamic topology assigns integer charges to equilibrium branches as zeros of an off-shell reservoir-mismatch one-form. We formulate this construction for a specified thermodynamic potential, active variables, fixed reservoir intensities and admissible compactified state space. The total charge is its Brouwer degree, equivalently the Morse degree of the potential and the oriented intersection number of the equation-of-state and reservoir Lagrangians. Regular Legendre changes of polarization preserve this degree after orientation transport; this covariance does not imply ensemble independence. We prove homotopy rigidity and boundary-jump formulae and relate auxiliary-angle windings, residues and gradient-flow representatives to the same degree. Standard Schwarzschild, Schwarzschild–AdS, fixed-charge RN–AdS, BTZ and logarithmically corrected examples follow from endpoint data. For grand-canonical RN–AdS and dyonic sectors, a positive-determinant desingularization of the coupled charge coordinates extends smoothly to zero size and identifies |Φ0|=1 and Φe2+Φm2=1 as boundary walls of the reservoir intersection problem, not local-stability walls or coordinate artifacts. A mixed dyonic window realizes the Poincaré–Hopf count on the physical fluctuation plane. In Kerr–Newman–AdS, one reservoir supports a coupled size–spin saddle and a companion minimum. At the saddle both diagonal curvatures in the extensive (S, J) variables are positive, whereas the Hessian determinant is negative. Thus the restricted radius index is +1 while the full fixed-potential Hessian index is −1, exhibiting information accessible only on the multi-variable fluctuation space.
The existence of massive particle surfaces can be inferred from the constancy of the quotient between energy and mass, the so called master equation. In this article we present a study of the massive particle surfaces of traversable wormholes. We use a purely a geometric approach based in the curvatures of a 2-dimensional Riemannian metric obtained by projecting the spacetime metric over surfaces of constant energy. Using the asymptotic and near throat limits of geodesic curvature, together with the sign of the Gaussian curvature we are able to determine the existence of LR’s and TCO’s and analyze its stability. We show that the general definition of a wormhole throat, namely the characterization of the throat in terms of a 2–dimensional constant-time hypersurface of minimal area, is equivalent to the conditions over the geodesic and Gaussian curvature, allowing for a general definition of a wormhole throat. We analyze in detail the Morris-Thorne family of wormholes and the Damour-Solodukhin wormholes. In the first case there is not a massive particle surface, while in the second there are more than one place where it can form. We show that for the wormholes considered there is always an odd number of light rings, one of them at the throat. In the case of Morris-Thorne wormhole our method leads to a procedure for building a wormhole with more than one LR. We study how the procedure can be extended to other wormhole spacetimes.
The f(R, T, Y) gravity is a modified theory that involves the Ricci scalar R, the trace of the energy-momentum tensor T, and the non-minimal matter geometry coupling term Y=RabTab. In this article, we are eager to explore the imprints of f(R, T, Y) cosmology on the early universe through the observational constraints of Big Bang nucleosynthesis. To analyze the early universe scenario, we investigate the deviation of freeze-out temperature through the ratio |ΔTf/Tf| that has observation limits |ΔTf/Tf|≤4.7×10−4 and the primordial helium mass fraction Yp of the light nuclear species having observational limits Yp=0.245±0.003. For instance, we consider two models f(R,T,Y)=R+αY and f(R,T,Y)=R+αY+γT to evaluate the viability of observational limits. We analyzed these models for the radiation-dominated era (ρ=3p) in the early universe. Our findings indicate that f(R, T, Y) gravity can agree with recent observational bounds on big bang nucleosynthesis via deviations in freeze-out temperature and primordial helium abundances, leading to a viable cosmology in the early cosmic epoch.
The aim of this study was to assess the potential of FTIR spectroscopy for monitoring biochemical changes in serum samples of individuals with carotid atherosclerosis following surgical intervention. Principal Component Analysis (PCA) of FTIR spectra from serum samples reveals distinct biochemical patterns at different time points: pre-surgery, 24 h post-surgery, and 48 h post-surgery. Two spectral ranges, 800–1800 cm−1 and 2800–3000 cm−1, were analyzed. PCA demonstrated that pre-surgery samples can be clearly differentiated from those taken 24 and 48 h post-surgery. However, no significant distinction was found between the 24-hour and 48-hour post-surgery samples. For the 800–1800 cm−1 range, the first principal component (PC1) explained 77.49% of the variance, highlighting the molecular vibrations of lipids, proteins, and carbohydrates. In the 2800–3000 cm−1 range, PC1 accounted for 94.89% of the variance, primarily reflecting lipid-related vibrations. These findings indicate a clear separation between pre-surgery and post-surgery samples, with the most significant variance explained by PC1. Additionally, the Boruta algorithm identified a key spectral range between 1506 cm−1 and 1673 cm−1, critical for distinguishing the samples. Classification models, including k-Nearest Neighbors, Gradient Boosting, Support Vector Machine, and Neural Network, demonstrated excellent performance in differentiating pre-surgery and post-surgery samples. However, the models struggled to distinguish between the 24-hour and 48-hour post-surgery time points. This suggests that FTIR spectroscopy may be useful for monitoring post-surgery recovery in carotid artery atherosclerosis, although subtle changes in the biochemical profile are challenging to detect between 24 and 48 h post-surgery.
Attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) provides information on the molecular composition and structure of samples. The use of ATR-FTIR was evaluated for biochemical analysis and taxonomic differentiation of entomopathogenic nematodes (EPNs). Spectra were obtained from a small sample (pellet) of a nematode population recovered from commercial EPN packages, which was placed directly on the ATR plate. Differences in signal intensity at multiple peaks associated with biomolecules critical to the survival of EPN (trehalose, glycogen, and triglyceride) were measured and visualized using Non-Metric Multidimensional Scaling (nMDS) and Principal Component Analysis (PCA). Statistically significant differences in peak signal intensity were observed between EPN species for each biochemical parameter, providing a basis for assessing the likelihood of their performance success in the field conditions. The present study also evaluated FTIR analysis of EPN for taxonomic differentiation. Results demonstrate that FTIR can be used to identify and differentiate Steinernema and Heterorhabditis genera/species, offering a potentially faster, less expensive alternative to molecular identification techniques. Ultimately, this study demonstrates the efficacy of ATR-FTIR as a reliable method for assessing the biochemical suitability of EPN products for field applications and differentiating between EPNs.
Endometrial cancer (EC) is increasingly prevalent worldwide, highlighting the need for non-invasive blood-based diagnostic triage tools. ATR-FTIR spectroscopy enables rapid, label-free biochemical profiling of plasma or serum for experimental cancer detection. To date, no systematic review or meta-analysis has evaluated the experimental performance of infrared spectroscopy for discriminating EC from non-cancer in blood-based samples. This study synthesizes available evidence to characterize the strength, consistency, and heterogeneity of the underlying spectroscopic signal across preclinical and proof-of-concept studies. MEDLINE, Web of Science, EMBASE, Scopus, Google Scholar, and CENTRAL were searched without language restrictions. Eligible studies evaluated ATR-FTIR spectroscopy of plasma or serum using histopathology as the reference standard. Pooled sensitivity, specificity, likelihood ratios, and diagnostic odds ratios were estimated using a bivariate random-effects model, with assessment of heterogeneity, threshold effects, and publication bias. Five case–control studies comprising 1376 participants were included. For plasma-based analyses, pooled sensitivity was 0.61 (95% CI: 0.59–0.68) and specificity was 0.73 (95% CI: 0.69–0.76), with a diagnostic odds ratio of 4.23 (95% CI: 3.33–5.37). For serum-based analyses, pooled sensitivity and specificity were both 0.62 (95% CI: 0.59–0.65), with a diagnostic odds ratio of 2.65 (95% CI: 2.16–3.25). Substantial heterogeneity and significant threshold effects were observed. Current evidence supports reproducible spectroscopic differences between EC and non-cancer blood samples under experimental conditions. However, methodological heterogeneity and retrospective case–control study designs limit clinical interpretability. These findings provide a benchmark for future prospective validation rather than immediate clinical application.
We present a nonsingular bouncing cosmological model in the framework of modified f(R,T) gravity within a spatially flat Friedmann–Robertson–Walker universe. A logarithmic time-dependent scale factor is assumed to realize a smooth transition from a contracting phase to an expanding phase without encountering an initial singularity. Based on this assumption, the dynamical evolution of the Hubble parameter, deceleration parameter, energy density, and pressure is obtained for various choices of the model and the matter–geometry coupling parameter to confirm the occurrence of a successful bounce. The effective equation of state parameter is examined to characterize the cosmic fluid during different evolutionary phases. The violation of energy conditions, necessary for the realization of the bouncing behavior, is also discussed. The stability of the model is investigated using the squared speed of sound and is found to remain positive within the allowed parameter space, indicating classical stability. Furthermore, constraints on the matter–geometry coupling parameter are obtained by demanding positive energy density, negative pressure, and a viable cosmological evolution. The obtained cosmological constraint on the coupling parameter is also shown to be compatible with the currently available compact-object constraints. The thermodynamic behavior of the model is examined by testing the generalized second law of thermodynamics. The total entropy production rate remains negative during the contracting phase and changes its sign to positive during the expanding phase. However, it becomes singular at the bouncing point, reflecting the breakdown of the standard thermodynamic description during the transition phase.
The energy extraction from the rotating black hole (BH) surrounded by the Dehnen-type dark matter (DM) halo is explored. Firstly, we obtain an axially symmetric BH spacetime metric using the Newman-Janis algorithm and then analyze the spacetime singularity by defining the Kretschmann scalar. Moreover, we numerically verify that the null, weak, dominant and strong energy conditions are satisfied within the parameter domain explored in this work. We then turn to investigate the effect of spacetime parameters on the behavior of the event horizon and ergosphere of the BH. The results indicate that the values of both event horizon and ergosphere radii increase under the influence of the DM halo parameters. Also, the timelike geodesics are studied by using the Lagrangian formalism. In particular, we analyze the impact of DM halo parameters on the constants of motion for massive neutral particles. It was found that the axial component of the specific angular momentum slightly increases with the rise of the DM halo parameters and vice versa for specific energy. In addition, we study the energy extraction processes, which are the Penrose process and the Blandford-Znajek mechanism. Our results show that the values of the energy efficiency of the Penrose process and the jet power of the Blandford-Znajek mechanism decrease with the rise of the density and radius of the DM halo, while the BH’s spin plays a key role in the energy extraction.
We apply the intertwiner operator method of arXiv:2411.08865 to topological field theories, including BF theories, Chern-Simons theory, and three-dimensional gravity. We construct the operator on foliated manifolds while preserving covariance on the Cauchy surface, and compare canonical and holomorphic quantization, providing the intertwiner in both frameworks. For three-dimensional gravity, we present both covariant and time-gauge formulations, analyze the constraints, and construct the corresponding intertwiner. As an application, we derive the path ordering of Wilson loops in Chern-Simons theory. The study of observables is left for future work. (The intertwiner discussed here establishes a morphism between the respective Hilbert spaces on which the two BRST charges, Q0 and Q, act. This should be distinguished from the unrelated intertwiner operator used in loop quantum gravity.)
In this work, we investigate the solutions to the governing equations of the Yang–Mills–Higgs model coupled with a dilaton. These solutions describe energy-minimizing static spherically symmetric field configurations with unit topological charge. We analyze the equations for different values of the Higgs self-coupling parameter β. For any Higgs self-coupling parameter β > 0, we use a regularization method to obtain the full set of boundary conditions. In the weak coupling limit β → 0, we derive the monotonicity of the solutions. In the limit β → ∞, the governing system reduces to the equation governing a single dilaton field. We find that the Euler–Lagrange equation is equivalent to a first-order Bogomol’nyi–Prasad–Sommerfield (BPS) equation, which admits an explicit solution. Furthermore, for any β > 0, we derive the energy bounds using the monotonicity of the energy function with respect to β and calculate the magnetic charge.
In particle physics the virtual N3LO contribution to gluon-fusion Higgs production in the Standard Model requires four-loop multi-scale QCD amplitudes that in dimensional regularization are dominated by singular integral reduction and difficult master-integral evaluations. In this note we show that a nonlocal UV completion makes each fixed-order four-loop Feynman diagram fully convergent in four dimensions while keeping the analytic structure needed for Lehmann–Symanzik–Zimmermann (LSZ) reduction formula. For gluon-fusion gg → H we derive a closed form Schwinger-parameter representation where all loop-momentum integrals are performed analytically and thus leaving finite parameter integrals viable for direct numerical evaluation without needing the usual UV subtractions. This method heps to isolate the collider-hard contribution as a convergent four-loop form factor. The strong coupling then is defined by a finite normalization condition in the entire-function regularization scheme and it is related to the MS‾ coupling by finite matching where after this matching, the regulator-dependent corrections decouple in the local limit EM → ∞.
In the late 1980s, Baulieu and Grossman demonstrated that the supersymmetric formulation of Langevin stochastic differential equations (SDEs), proposed earlier by Parisi and Sourlas, belongs to the family of Witten-type topological field theories (TFTs). From a certain angle, this finding may appear puzzling: TFTs have no local degrees of freedom, whereas SDEs do exhibit local fluctuations. In this paper, we address this apparent contradiction in the context of the supersymmetric theory of stochastic dynamics, a generalization of the Parisi–Sourlas-Baulieu-Grossman approach to SDEs of arbitrary form. The resolution lies in recognizing that, as a mathematical construct, each SDE encodes two subsystems: the continuous-time dynamical system (DS) and its noise. The Parisi–Sourlas construction employs a gauge-fixing procedure to rewrite the partition function of the noise (PFN) in terms of the variables of the DS, resulting in the Witten index. Being a topological invariant, this representative of the PFN is independent of the duration of the evolution, reflecting the absence of dynamics in the noise, as expected since the noise is a static probabilistic entity that experiences no backaction from the DS. The partition function of the DS itself is obtained by twisting, i.e., by imposing anti-periodic boundary conditions (APBC) on the Faddeev–Popov ghosts, thereby rendering them physical – a step that can be justified by interpreting the ghosts, e.g., as differentials used in numerical experiments to track Lyapunov exponents. Since APBC are not compatible with the topological character of the Witten index, one might be tempted to conclude that the twist destroys the topological/BRST supersymmetry (TS) of the model altogether. In the context of stochastic dynamics, however, this conclusion is incorrect. The TS remains intact because it is a property of the stochastic evolution operator (SEO), the fundamental construct corresponding to open boundary conditions and known in DS theory as the generalized transfer operator. The Witten index and the partition function do not define different models; rather, they are different objects of the same model defined by the SEO. What APBC do change, however, is that the partition function exhibits exponential growth in time when TS is spontaneously broken – a situation that, as it turns out, is equivalent to the definition of chaos in random DSs introduced by Ruelle. Within the resulting picture of chaos, 1/f noise emerges as a consequence of the Goldstone theorem, while the butterfly effect is described by an effective field theory that may possess a hidden topological structure, as we speculate on the basis of the Ginzburg-Landau approach and AdS/CFT duality.
We show that chiral matters in the minimal supersymmetric standard model (MSSM) with semi-realistic flavor structures can be obtained from 7-brane configurations of magnetized super Yang-Mills (SYM) theory on a toroidal orbifold R1,3×(T2)3/(Z2×Z2′), where background magnetic fluxes and Wilson-lines are turned on preserving four-dimensional N=1 supersymmetry. The zero-mode spectrum of chiral multiplets in total is just MSSM ones, except the existence of those for three generations of right-handed neutrino and extra generations of MSSM Higgs pairs.Hierarchical Yukawa couplings can be obtained from the overlap integrals of wavefunctions localized in extra dimensions, allowing semi-realistic patterns of flavor structures for quarks and charged leptons. We also develop a systematic way to embed additional 7-branes into the configuration, those are sequestered from the visible sector toward a hidden sector model building.
In the standard formulation of chiral Lagrangians and Stueckelberg extensions, the use of the unitary field U=eiπ/f together with explicit power counting in 1/f guarantees a finite operator basis at any fixed mass dimension. This work does not challenge that well-established physical fact. Instead, we investigate a subtle algebraic phenomenon that arises when one adopts the logarithmic (exponential) parametrisation π (with f absorbed) in automated operator enumeration algorithms.We show that the expansion of the Maurer–Cartan form Ω=U−1dU in powers of π generates an infinite tower of local densities that remain independent in the integration-by-parts (IBP) quotient when treated as elements of a filtered completion of the local jet algebra. This non-Noetherian behaviour signals a potential failure mode for polynomial Hilbert-series methods if the allowed function class is not explicitly declared.Our main contribution is a systematic diagnostic tool — a separating-functional lemma and an explicit SU(2) witness — that determines when such infinite towers survive IBP reduction. This diagnostic serves as a practical warning for developers of automated EFT codes: the finiteness of an operator basis depends on the choice of field parametrisation and the function class fed into the algorithm.
