We consider pseudo Nambu-Goldstone bosons arising from Dirac fermions transforming in real representations of a confining gauge group as dark matter candidates. We consider a special case of two Dirac fermions and couple the resulting dark sector to the Standard Model using a vector mediator. Within this construction, we develop a consistent low energy effective theory, with special attention to Wess-Zumino-Witten term given the topologically non-trivial coset space. We furthermore include the heavier spin-0 flavour singlet state and the spin-1 vector meson multiplet, by using the Hidden Local Symmetry Lagrangian for the latter. Although we concentrate on special case of two flavours, our results are generic and can be applied to a wider variety of theories featuring real representations. We apply our formalism and comment on the effect of the flavour singlet for dark matter phenomenology. Finally, we also comment on generalisation of our formalism for higher representations and provide potential consequences of discrete symmetry breaking.

We compute the electron spin susceptibility in the pseudogap regime of the two-dimensional Hubbard model in the framework of a SU(2) gauge theory of fluctuating magnetic order. The electrons are fractionalized in fermionic chargons with a pseudospin degree of freedom and bosonic spinons. The chargons are treated in a renormalized mean-field theory and order in a Néel or spiral magnetic state in a broad range around half filling below a transition temperature T * . Fluctuations of the spin orientation are captured by the spinons. Their dynamics is governed by a nonlinear sigma model, with spin stiffnesses computed microscopically from the pseudospin susceptibility of the chargons. The SU(2) gauge group is higgsed in the chargon sector, and the spinon fluctuations prevent breaking of the physical spin symmetry at any finite temperature. The electron spin susceptibility obtained from the gauge theory shares many features with experimental observations in the pseudogap regime of cuprate superconductors: the dynamical spin susceptibility S ( q , ω ) has a spin gap, the static uniform spin susceptibility κ s decreases strongly with temperature below T * , and the NMR relaxation rate T 1 − 1 vanishes exponentially in the low temperature limit if the ground state is quantum disordered. At low hole doping, S ( q , ω ) exhibits nematicity below a transition temperature T nem < T * , and at larger hole doping in the entire pseudogap regime below T * .

Objective: To compare mean duration of analgesia when 1mg Nalbuphine is added to 15mg of Bupivacaine 0.75% versus 15mg of Bupivacaine 0.75% alone in spinal anesthesia for infraumbilical surgeries. Study Design: Randomized Controlled Trial. Setting: Department of Anesthesia, Allied Hospital, Faisalabad. Periods: April 2024 to October 2024. Methods: Total 60 subjects undergoing elective infraumbilical surgery under spinal anesthesia were assigned to two groups; Group A received inj. 0.75% Bupivacaine 15mg along with inj. Nalbuphine 1mg (0.1ml) in subarachnoid space via 25 gauge Quinke type spinal needle and Group B received 0.75% bupivacaine 15mg alone in subarachnoid space using 25guage spinal needle. Analgesia duration (hours) was calculated from sensory block onset to first request of analgesia using VAS score. Analysis of data was done using SPSS.23, for statistical significance p-value ≤0.05 was taken. Results: Sensory and motor block onset in Group A vs B noted was 3.25 ± 0.41 minutes & 6.36 ± 0.66 minutes vs 4.31 ± 0.39 minutes & 7.90 ± 0.63 minutes (p<0.001). Duration of postoperative analgesia was longer in Group A 5.77 ± 0.57 hours vs 5.03 ± 0.29 hours in Group B (p < 0.001). Conclusion: These findings suggest that intrathecal Nalbuphine added to Bupivacaine can considerably prolonged the duration of analgesia versus when Bupivacaine used alone in spinal anesthesia for infraumbilical surgeries irrespective of age, gender, or comorbidity status.

Modern physics confronts a crisis of arbitrariness: the Standard Model requires approximately 19 'free parameters' that must be measured experimentally and inserted by hand, offering no explanation for their provenance. To the physicist, these numbers appear accidental; to the theologian, this apparent arbitrariness presents a crisis of teleology. If the fundamental constants of creation are random, where is the imprint of the Logos? This paper proposes a 'Digital Ontology' rooted in S21 Vacuum Manifold Theory. We demonstrate that the structure of the physical universe emerges as the topological inevitability of a simple, parameter-free binary code. Starting from a 6-bit lattice (the 64 states, anciently mapped in the I Ching), we show that exactly 21 configurations are mathematically stable, forming a vacuum manifold that uniquely determines the gauge groups, coupling constants, and particle content of the Standard Model. The theory has been experimentally validated: the JUNO collaboration's 2025 measurement of the solar neutrino mixing angle (sin²θ₁₂ = 0.309 ± 0.003) matches the S21 prediction of (φ-1)/2 = 0.309017 within 0.02σ deviation. We further demonstrate that the sacred numbers recurring across wisdom traditions—3, 7, 10, 21, 64, φ—are not arbitrary cultural choices but reflections of actual vacuum topology. The apparent differences between the Vedic concept of Brahman, the Islamic doctrine of Tawhid, the Kabbalistic Sefirot, Buddhist Śūnyatā, and the Christian Logos dissolve when viewed as projections of the same hyperdimensional truth. Keywords: vacuum topology, fine-tuning, Logos, theodicy, sacred numbers, Standard Model, multiverse, I Ching, digital ontology

The cosmological constant (CC, Λ) problem stands as one of the most profound puzzles in the theory of gravity, representing a remarkable discrepancy of about 120 orders of magnitude between the observed value of dark energy and its natural expectation from quantum field theory. This paper synthesizes two innovative paradigms—holographic naturalness (HN) and pre-geometric gravity (PGG)—to propose a unified and natural resolution to the problem. The HN framework posits that the stability of the CC is not a matter of radiative corrections but rather of quantum information and entropy. The large entropy SdS∼MP2/Λ of the de Sitter (dS) vacuum (with MP being the Planck mass) acts as an entropic barrier, exponentially suppressing any quantum transitions that would otherwise destabilize the vacuum. This explains why the universe remains in a state with high entropy and relatively low CC. We then embed this principle within a pre-geometric theory of gravity, where the spacetime geometry and the Einstein–Hilbert action are not fundamental, but emerge dynamically from the spontaneous symmetry breaking of a larger gauge group, SO(1,4)→SO(1,3), driven by a Higgs-like field ϕA. In this mechanism, both MP and Λ are generated from more fundamental parameters. Crucially, we establish a direct correspondence between the vacuum expectation value (VEV) v of the pre-geometric Higgs field and the de Sitter entropy: SdS∼v (or v3). Thus, the field responsible for generating spacetime itself also encodes its information content. The smallness of Λ is therefore a direct consequence of the largeness of the entropy SdS, which is itself a manifestation of a large Higgs VEV v. The CC is stable for the same reason a large-entropy state is stable: the decay of such state is exponentially suppressed. Our study shows that new semi-classical quantum gravity effects dynamically generate particles we call “hairons”, whose mass is tied to the CC. These particles interact with Standard Model matter and can form a cold condensate. The instability of the dS space, driven by the time evolution of a quantum condensate, points at a dynamical origin for dark energy. This paper provides a comprehensive framework where the emergence of geometry, the hierarchy of scales and the quantum-information structure of spacetime are inextricably linked, thereby providing a novel and compelling path toward solving the CC problem.

A bstract In this article, we work out some variations on the discussion of the C-field flux densities in the Sati-Schreiber program. We start by explaining the need for global completion of the field content: the fluxes, the gauge potentials and the gauge transformations on the worldvolume of a single M5 brane in eleven-dimensional supergravity, and how this is encoded by the choice of flux quantization law. Assuming Hypothesis H that the 4-flux in M-Theory is flux quantized in a non-abelian cohomology theory called 4-cohomotopy, and the three-flux on the M5 brane worldvolume in (twisted) 3-cohomotopy, we generalize some previous calculations known in the literature to include twisting by background gravity and placing M5 branes on orbifolds. We show that the null concordances of cohomotopically charged fluxes give rise to the traditional gauge potentials and the null concordances of concordances give rise to the corresponding gauge transformations via surjections, in the cases of tangentially twisted cohomotopy, twistorial cohomotopy and equivariant twistorial cohomotopy. We construct the surjections explicitly for these cases and check the consistency relations with the corresponding Bianchi identities. Thus, we show how the traditional formulas for the local gauge potentials on M5 brane worldvolume on curved spacetimes and orbifolds are indeed reproduced by the homotopy theory and, as such, become amenable to global completion in cohomotopical charge quantization.

A bstract We investigate conformal field theories with gauge group U( N ) at arbitrary rank N , focusing on the role of trace relations in determining the structure of the Hilbert space. Working in the free trace algebra without imposing relations, we identify a class of evanescent states that vanish at finite N . Using the Koszul complex of [1], we implement trace relations systematically via ghosts and a fermionic charge Q b . This framework allows us to define and compute transition amplitudes between evanescent and physical states, which we show correspond precisely to ordinary CFT amplitudes analytically continued in N . Our results provide a direct algebraic realization of the proposals which realize trace relations in the bulk as over-maximal giant gravitons [1–3] and establish analytic continuation in N as a powerful tool for understanding finite- N effects.

A bstract This paper develops a framework for the Hamiltonian quantization of complex Chern-Simons theory with gauge group $$\text{SL}(2,{\mathbb{C}})$$ at an even level $$k\in {\mathbb{Z}}_{+}$$ . Our approach follows the procedure of combinatorial quantization to construct the operator algebras of quantum holonomies on 2-surfaces and develop the representation theory. The *-representation of the operator algebra is carried by the infinite dimensional Hilbert space $${\mathcal{H}}_{\overrightarrow{\lambda }}$$ and closely connects to the infinite-dimensional *-representation of the quantum deformed Lorentz group $${\mathcal{U}}_{\text{q}}\left(s{l}_{2}\right)\otimes {\mathcal{U}}_{\widetilde{\text{q}}}\left(s{l}_{2}\right)$$ . The quantum group $${\mathcal{U}}_{\text{q}}\left(s{l}_{2}\right)\otimes {\mathcal{U}}_{\widetilde{\text{q}}}\left(s{l}_{2}\right)$$ also emerges from the quantum gauge transformations of the complex Chern-Simons theory. Focusing on a m -holed sphere Σ 0, m , the physical Hilbert space $${\mathcal{H}}_{\text{phys}}$$ is identified by imposing the gauge invariance and the flatness constraint. The states in $${\mathcal{H}}_{\text{phys}}$$ are the $${\mathcal{U}}_{\text{q}}\left(s{l}_{2}\right)\otimes {\mathcal{U}}_{\widetilde{\text{q}}}\left(s{l}_{2}\right)$$ -invariant linear functionals on a dense domain in $${\mathcal{H}}_{\overrightarrow{\lambda }}$$ . Finally, we demonstrate that the physical Hilbert space carries a Fenchel-Nielsen representation, where a set of Wilson loop operators associated with a pants decomposition of Σ 0, m are diagonalized.

We discuss a one-parameter non-Abelian GLSM with gauge group (U(1)× U(1)× U(1))\rtimes\mathbb{Z}_3 ( U ( 1 ) × U ( 1 ) × U ( 1 ) ) ⋊ ℤ 3 and its associated Calabi-Yau phases. The large volume phase is a free \mathbb{Z}_3 ℤ 3 -quotient of a codimension 3 3 complete intersection of degree- (1,1,1) ( 1 , 1 , 1 ) hypersurfaces in \mathbb{P}^2×\mathbb{P}^2×\mathbb{P}^2 ℙ 2 × ℙ 2 × ℙ 2 . The associated Calabi-Yau differential operator has a second point of maximal unipotent monodromy, leading to the expectation that the other GLSM phase is geometric as well. However, the associated GLSM phase appears to be a hybrid model with continuous unbroken gauge symmetry and cubic superpotential, together with a Coulomb branch. Using techniques from topological string theory and mirror symmetry we collect evidence that the phase should correspond to a non-commutative resolution, in the sense of Katz-Klemm-Schimannek-Sharpe, of a codimension two complete intersection in weighted projective space with 63 63 nodal points, for which a resolution has \mathbb{Z}_3 ℤ 3 -torsion. We compute the associated Gopakumar-Vafa invariants up to genus 11 11 , incorporating their torsion refinement. We identify two integral symplectic bases constructed from topological data of the mirror geometries in either phase.

This study explores a minimal Standard Model extension featuring a dark sector with an SU(2) gauge group. The three dark gauge bosons, stabilized by a custodial symmetry triggered by an additional scalar doublet, serve as dark matter candidates. After applying current experimental constraints, we analyze the phase transition dynamics and compute the resulting stochastic gravitational-wave background. We identify regions of parameter space that simultaneously yield the observed dark matter relic density and produce a strong first-order phase transition, the gravitational-wave signal from which is detectable by future observatories like LISA, DECIGO, BBO, TianQin, or Taiji.

A bstract We investigate the anomalies of 6d $$ \mathcal{N} $$ N = (2, 0) superconformal field theories for any ADE gauge group using the modern characterization of anomalies by cobordism. We propose that, in order to account for all features of the anomaly, a bordism theory with exotic tangential structure is needed. We then attempt to match the anomaly in the IR effective theory on the tensor branch with a suitable WZW term. Once again, we show that the exotic bordism structure is necessary to achieve this. Our results suggest a natural explanation for the origin of the Hopf-Wess-Zumino term.

A bstract This work studies the connection of the global properties of the SM gauge group to 1-form discrete symmetries, the possible non-Abelian embeddings of the SM group, and electric and magnetic charge quantisation. Building on previous work, we introduce indexes to characterise the group choices, connect the concept of compositeness degree to emergent electric 1-form symmetry, introduce a new model to fill in the p = 1 gap, and analyse the magnetic spectrum while connecting its UV and IR realisations.

A bstract We consider an abelian extension of the Standard Model (SM) comprising a new gauge group U(1) ′ , with the neutral gauge boson Z′ having flavour violating couplings to quarks and leptons. The fermion content is the same as in SM except for the addition of three right-handed neutrinos. The model, proposed in [1], describes the couplings of Z′ to fermions in terms of three rational parameters ϵ 1 , 2 , 3 that sum to zero imposing the cancellation of the gauge anomalies. Each ϵ i is common to all fermions in a generation, a feature producing correlations among quark and lepton observables. We focus on $$b\to s{{\ell}}_{1}^{-}{{\ell}}_{2}^{+}$$ transitions for the lepton flavour conserving ℓ 1 = ℓ 2 and lepton flavour violating case ℓ 1 ≠ ℓ 2 . Small deviations with respect to the SM predictions are found in the first case, which reflects a feature of the model where quark and lepton sectors prevent each other to manifest large discrepancies with respect to SM. We investigate the correlations between rare B and B s decays and the leptonic processes τ − → μ − μ + μ − , μ − → e − γ , μ − → e − e + e − and the μ − → e − conversion in nuclei. We show that the current experimental upper bounds on these four channels play an increasingly important role in constraining the branching fractions of lepton flavour violating B and B s decays. While the present bound on τ − → μ − μ + μ − does not impose significant restrictions, the other three modes set progressively more stringent limits, an important information for the planned new experimental facilities.

A bstract We develop a gauge invariant, Loop-String-Hadron (LSH) based representation of SU(2) Yang-Mills theory defined on a general graph consisting of vertices and half-links. Inspired by weak coupling studies, we apply this technique to maximal tree gauge fixing. This allows us to develop a fully gauge-fixed representation of the theory in terms of LSH quantum numbers. We explicitly show how the quantum numbers in this formulation directly relate to the variables in the magnetic description. In doing so, we will also explain in detail how the Kogut-Susskind formulation, prepotentials, and point splitting work for general graphs. In the appendix of this work, we provide a self-contained exposition of the mathematical details of Hamiltonian pure gauge theories defined on general graphs.

A bstract We propose SL(2, ℤ) dualities of supersymmetric boundary conditions in the three-dimensional supersymmetric field theories describing a semi-infinite M2-brane terminating on M5-branes. Specifically, we present dualities of boundary conditions for Abelian (quiver) ADHM theories and circular quiver Chern-Simons matter theories including the ABJM model. For the circular quiver Chern-Simons theories we take boundary conditions breaking a U(1) 1 × U(1) −1 gauge group to its diagonal subgroup which is decoupled. This can be generalized to break U(1) k × U(1) − k , leaving a ℤ k gauge theory. We find matching of the ’t Hooft anomalies and supersymmetric half-indices for all the proposed dual boundary conditions.

Higher rank gauge theories are generalizations of electromagnetism where, in addition to overall charge conservation, there is also conservation of higher rank multipoles such as the total dipole moment. In this work we study a four-dimensional lattice tensor gauge theory coupled to bosonic matter which has second rank tensor electric and magnetic fields and charge conservation on individual planes. Starting from the Hamiltonian, we derive the lattice action for the gauge fields coupled to q = 1 , 2 charged scalars. We use the action formulation to carry out Monte Carlo simulations to map the phase diagram as a function of the gauge ( β ) and matter ( κ ) couplings. We compute the nature of correlators at strong and weak coupling in the pure gauge theory and compare the results to numerical simulations. Simulations show that the naive weak coupling regime (small κ , large β ) does not survive in the thermodynamic limit. Instead, the strong coupling confined phase spans the whole phase diagram. It is a proliferation of instantons that destroys the weak coupling phase and we show, via a duality transformation, that the expected strong confinement is present in the analog of Wilson line correlators. For finite matter coupling at q = 1 we find a single thermodynamic phase albeit with a first-order phase transition terminating in a critical end point. For q = 2 it is known that the X-cube model with Z 2 fractonic topological order is recovered deep in the Higgs regime. The simulations indeed reveal a distinct Higgs phase in this case.

We study Kitaev’s quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations which can be identified with equivalence classes of ‘localized and transportable endomorphisms’, which produce anyonic excitations from the ground state. Following the Doplicher–Haag–Roberts (DHR) sector theory from AQFT, we organize these endomorphisms into a braided monoidal category capturing the fusion and braiding properties of the anyons. We show that this category is equivalent to textbf{Rep}_f {{mathcal {D}}}(G), the representation category of the quantum double of G. This establishes for the first time the full DHR structure for a class of 2d quantum lattice models with non-abelian anyons.

A bstract Local supersymmetries have been a guiding principle to construct smooth horizonless supergravity solutions. By computing brane densities from the brane low-energy effective action, we classify the BPS solutions that have the maximal local supersymmetry structure, with sixteen supersymmetries. We find that whenever the gauge group is broken to its maximal abelian subgroup, the brane construction becomes purely geometric and one can identify the preserved local supercharges. This class of solution includes two- and three-charge monopoles, and polarised branes. On the contrary, we show that instantons involve pure non-abelian degrees of freedom that cannot have a geometric interpretation. Hence, we conjecture that such instantons cannot be fully captured by supergravity.

In this study, we conduct a thorough examination of the spectrum of the open confining string in 3 + 1 dimensions, commonly referred to as the open flux tube, across various gauge groups of S U ( N c ) . Our primary objective is to explore its behavior as we approach the large- N c limit and the identification of possible world-sheet axion states. Specifically, we undertake a detailed analysis of the associated spectrum for N c = 3 , 4, 5, 6. This marks the first systematic investigation of the open flux-tube spectrum within the context of the large- N c limit. More specifically, we analyze the spectra of flux tubes that form between a static quark-antiquark pair, considering a significant number of radial excitations and eight irreducible representations characterized by the quantum numbers of angular momentum Λ , charge conjugation and parity η C P , and the reflection symmetry ε for Λ = 0 . To this purpose we employ a diverse set of suitable operators, an anisotropic action, and smearing techniques, and solve the generalized eigenvalue problem. We compare our findings with predictions from the Nambu-Goto string model to assess potential tensions indicative of novel phenomena such as the existence of axionlike state along the flux-tube world sheet. Notably, we provide undoubted evidence of the existence of a massive axionlike particle with the same mass as the corresponding axion extracted within the context of closed flux tube. This strengthens the conjecture that the axion is a property of the world sheet of the QCD string.

Leptogenesis via axion oscillation after inflation is an alternate mechanism of thermal leptogenesis. In this mechanism, the requirement of the existence of a lepton number ( L ) violating process in equilibrium to drive the lepton number requires the temperature of leptogenesis to be at ∼ 10 13 GeV . Triplet scalars, due to their interaction with gauge bosons, make a suitable candidate to prevail in the thermal bath via gauge scattering at such a high energy. Also, owing to its interaction with Standard Model (SM) leptons and the Higgs scalar, it can mediate the Δ L = 2 process. Moreover, just one triplet is enough to serve the purpose as opposed to thermal leptogenesis where at least one more triplet scalar/right-handed neutrino is required to generate a sizable C P violation. In this work, we study a model where the SM gauge group is extended with U ( 1 ) PQ , with the addition of one Higgs doublet, one scalar triplet, and one complex scalar singlet. The presence of a complex scalar singlet decouples the Peccei-Quinn (PQ) symmetry breaking from the electroweak scale. It also provides a common source of an axionlike particle and seesaw scale. The scalar triplet offers a common link between leptogenesis via axion oscillation and neutrino mass. Further, with the presence of one triplet scalar, the lepton flavor violation process is directly determined from low-energy neutrino oscillation data.