Papers

We investigate the entropy of a dynamical black hole arising from second-order perturbations of a general stationary background with a bifurcate Killing horizon. Using Gaussian null coordinates, we study the geometry of the apparent horizon perturbatively up to second order. Within the covariant phase space formalism, to explore the contribution of matter fields, we introduce a new modified canonical energy, and establish a balance law relating the second-order variation of the entropy to the energy flux entering the black hole. We show that the entropy is given precisely by the area of the apparent horizon at second order when the null energy condition holds for the infalling matter, and that the variation of the entropy also obeys the second law. We also discuss the possibility that the area law continues to hold when the null energy condition is violated.

We present a combined determination of charged-pion and charged-kaon fragmentation functions (FFs), denoted HAPS-PiFF1.0 and HAPS-KaFF1.0, at next-to-leading order (NLO) and within a next-to-next-to-leading-order (NNLO) perturbative QCD setup. The analysis combines single-inclusive electron-positron annihilation (SIA) data with charge-separated semi-inclusive deep-inelastic-scattering (SIDIS) multiplicities from HERMES and COMPASS. A central goal of this work is to incorporate the modern COMPASS SIDIS input, namely the COMPASS 2025 proton-target multiplicities and the COMPASS 2026 revised isoscalar-target multiplicities, into a common charged-pion and charged-kaon FF analysis and to assess their role in the resulting flavor separation. The revised isoscalar data supersede the earlier COMPASS measurements used in previous global fits. The charge-separated pion multiplicities provide important constraints on favored and unfavored light-quark fragmentation, while the kaon measurements enhance the sensitivity to light-quark, unfavored, and strange-to-kaon fragmentation channels. In both analyses, the gluon FF remains indirectly constrained in the present SIA+SIDIS framework and should be interpreted with appropriate caution. The extractions are carried out using the publicly available MontBlanc framework, and the resulting HAPS-PiFF1.0 and HAPS-KaFF1.0 replica sets are provided in the standard LHAPDF format.

Countless biological and physical systems experience fluctuations that exhibit non-trivial temporal correlations. The Unified Colored-Noise Approximation (UCNA) is a framework providing an approximate description of such stochastic dynamics with colored noise, valid in the limits of vanishing and infinite correlation time of the noise. We first pinpoint and address some criticalities in its original derivation, recasting the result through a time-scale separation procedure. By using our approach, we derive the next-to-leading order correction to the dynamics in both limiting regimes, and highlight the relevant physical scalings of these approximations. Our result helps frame the limits of validity of both the original and the refined formulas, especially in comparison with those derived through different approximation procedures. We show our findings in two paradigmatic examples, a quartic potential and a stochastic logistic growth with multiplicative noise.

We derive the Lehmann-Symanzik-Zimmermann reduction formalism for a massive spin-2 particle on Minkowski spacetime and extend the formalism to cosmological spacetimes. The reduction formalism allows for a versatile proof that the Goldstone boson equivalence theorem holds in Friedmann-Lemaître-Robertson-Walker space-times. For the de Sitter and the radiation filled universe, we investigate the Goldstone dynamics and perform an analysis of the range of validity provided by the effective kinetic operator.

Quasi-deterministic single-photon generation is a key requirement for many photonic quantum technologies. Photon sources based on spontaneous parametric down-conversion (SPDC) are widely used for producing high-quality photons; however, the probabilistic nature of the process limits the generation of synchronized multi-photon states. Here, we demonstrate temporal synchronization of multiple photon-generation events using a free-space-fiber hybrid delay line with feed-forward control, enabling fast and efficient switching and scalable operation. Narrow-band, telecom-wavelength photons compatible for fiber transmission are heralded from a monolithic cavity SPDC source and synchronized across 20 time bins. This yields a sixfold enhancement in synchronized rates and enables multi-photon synchronization, with only a marginal increase of higher-order photon-number contributions.

Engineers often measure many quantities-speed, pressure, temperature, length-expressed in different physical units. The Buckingham Pi-grec theorem states that these variables can always be combined into a smaller set of dimensionless numbers whose values fully determine the system's behaviour. Identifying the appropriate dimensionless groups has traditionally required expert knowledge and physical insight. This paper shows that they can instead be discovered automatically from data, without prior knowledge of the governing physics. The key observation is that, after logarithmic transformation, measurements collected under different scalings of the same system lie on a low-dimensional manifold whose geometry is determined by the underlying dimensionless groups. Singular value decomposition (SVD) identifies this manifold directly from data. A subsequent search over integer-exponent combinations recovers candidate dimensionless quantities, while a repeating-variable filter retains only those constructed from the machine's characteristic scales. This procedure recovers familiar engineering groups, including the flow coefficient, head coefficient, and Mach number, while excluding equivalent but less interpretable alternatives. The method is demonstrated on a synthetic compressor dataset containing 16,000 measurements. Starting from raw dimensional variables and no physics input, it recovers the correct dimensionless groups to numerical precision and reproduces the compressor performance map with an error below 0.01%. More broadly, the work reveals a close connection between classical dimensional analysis and modern data-driven learning. Both rely on the same underlying algebraic structure, suggesting new approaches for building physical models that are simultaneously interpretable, scalable, and data-efficient.

We present the EGIDE (The Edge-on Galaxies in the DESI survey) project - a catalogue of 149,215 edge-on galaxy candidates created using the data of the DESI Legacy Imaging Survey DR10 images. The catalogue size is ten times bigger than its predecessor and covers more than half of the sky. It is constructed in an automatic way utilizing the full power of manual annotations from the GalaxyZoo volunteers, implemented in the Zoobot neural model, which was fine-tuned to search for edge-on galaxies specifically. To ensure the credibility of the dataset, subsequent manual supervision was done. The EGIDE catalogue provides homogeneous SExtractor photometry in $griz$ bands, total stellar mass estimation, redshift values for 98% of the sample, star formation rates and other information. All of this is publicly available at The Edge-on Galaxy Database site. The preliminary analysis focused on differences between edge-on galaxies in the so-called blue sequence and red cloud populations. These galaxies demonstrate distinct properties: the number of redder galaxies drops with increasing $a/b$ ratio faster than for the bluer galaxies; galaxy thickness varies with galaxy colour: red sequence galaxies are thicker than blue cloud galaxies; the flattening ratio $q=b/a$ increases with total stellar mass $M_{\star}$ for the high-mass end. It is an intriguing result, that the same trend of $q$ increasing is detected from both the statistical models of figures of revolution and direct observations of edge-on galaxies in EGIDE independently. The full extent of the validity of this relationship can only be determined after correctly accounting for the contributions of the bulge and the PSF.

Recent discoveries of exotic hadrons, which cannot be classified within the conventional quark model of $q \bar{q}$ mesons and $qqq$ baryons, strongly imply the existence of dynamically generated hadronic molecules. Some of these hadron-hadron interactions are accompanied by coupled-channel effects, which remain challenging to quantitatively determine. In this work, we demonstrate that femtoscopy provides a sensitive probe of such coupled-channel dynamics. We calculate correlation functions for the double-strangeness pentaquark candidates $P_{css}(4493)$ ($J^P=1/2^-$) and $P_{css}(4633)$ ($J^P=1/2^-$ or $3/2^-$), revealing clear signatures of the attractive interactions that can form bound states. The results are markedly different from those obtained in scenarios that neglect off-diagonal transitions, highlighting the importance of coupled-channel effects for understanding the structure of these hadrons.

Metasurfaces and complex photonic components are increasingly co-designed with computational back-ends via end-to-end optimization, yet such optimizations are expensive and opaque – obscuring the role of the optics and any fundamental performance limits. We develop two information-theoretic objectives, based on Shannon capacity and Fisher information, that isolate the photonic contribution to image formation. Both are closed-form, data-free functions of the transfer matrix, requiring no training data, and yield designs whose reconstruction quality matches end-to-end optimization. We prove that for both objectives, and for a broader family with a shared mathematical structure, the optimal transfer matrix is a permutation matrix: each source's emission is concentrated on a single, distinct detector, a condition we call generalized focusing. This holds regardless of source/detector geometry, as we demonstrate in settings where conventional imaging intuition offers no guidance, including a two-way imager, imaging through a random scattering medium, and Hermite–Gauss mode sorting. The root of this constraint is an "intensity bottleneck": nonnegative intensity measurements admit only Kronecker deltas as a complete orthonormal basis. We further show that this bottleneck, and the generalized-focusing optimum, persist for coherent and partially coherent sources – the constraint is the detector array, not the source coherence.

Walk-in, picotesla-scale environments are essential for measurements of biomagnetism and fundamental physics. However, conventional rooms require typical active dynamic compensation, which adds complexity and magnetic noise. Here, we present a solution that achieves an absolute residual field well below 100$\,$pT within its central measurement volume. Following magnetic equilibration, this environment achieves picotesla-scale reproducibility. Consequently, optically pumped magnetometers operate at their design noise and drift performance and remain operational during sensor motion without active feedback. A key technique is robotic mapping, which resolves the ultra-low residual field patterns and demagnetization stability. We demonstrate the platform's versatility through high-fidelity adult and fetal magnetocardiography, standing magnetoencephalography, and ultra-low field magnetic resonance with polarized noble gases in the limit of strongly coupled spins in a negligible holding field. The achieved passive reproducibility turns the ultra-low magnetic background into a predictable, correctable property, establishing a novel foundation for next-generation quantum sensing and precision physics.

We present a structural analysis of glasses formed by mix of SiO2 and B2O3 glass formers with soda and lime modifiers (Na2O and CaO), which provide a good testing ground for Stochastic Agglomeration Theory. With local structural units properly identified, we can reproduce the one-parameter glass transition temperature T_g (z) curve for the family of (0.75-z) SiO_2 + 0.15 Na_2O + 0.10 CaO + z B_2O_3 glasses studied experimentally by Smedskjaer et al.

In this work we present an effective Lifshitz black hole solution with Born-Infeld electrodynamics and explore some of its properties. We discuss the mechanism for capturing the solution, achieved through diffeomorphism invariance breaking, study the emergent causal structure, and analyze aspects of critical behavior and local stability in the associated thermodynamics.

Motivated by the mirror symmetry for circle compactified 4d $N=2$ theories, we propose a geometric framework for studying the representation theory of non-admissible $W$-algebras $W^{k}(\mathfrak g,f)$ at levels $k=-h^\vee+\frac{1}{n}\frac{m}{u}$, using the geometry of generalized affine Springer fibers $Sp_{\nu}(\tilde{g},f)$ with slope $\nu=u/m$. The central proposal is that each non-empty $C^*$-fixed locus, labeled by a double coset $\tilde w\in W_\nu\backslash\tilde{W}/W_f$, gives rise to simple modules whose highest weight is determined by the map $\tilde w\mapsto\tilde w(k\Lambda_0+\tilde\rho)-\tilde\rho$, while the dimension of the fixed variety encodes additional non-semisimple structure (logarithmic modules). We verify this correspondence in numerous examples, including $D_4$, $E_6$, $E_8$, and twisted theories of type $^3D_4$ and $^2A_3$, where our geometric counting reproduces known results for both admissible and non-admissible $W$-algebras.

Existing methods for deciding whether a bipartite quantum state is separable or entangled typically fall into one of two categories: they are either complete but require access to an explicit density matrix followed by numerical optimization, or they can be evaluated directly by measuring the quantum system but are incomplete, in the sense that they cannot detect all forms of entanglement. In this work, we overcome both limitations in a unified framework. First, we bypass numerical optimization by deriving separability criteria in the form of universal bounds on tensor powers of separable states. We prove that these bounds are complete: every entangled state violates them for sufficiently large tensor powers. Second, we explicitly construct a corresponding complete family of nonlinear entanglement witnesses, which can detect all forms of entanglement without requiring an explicit density matrix. The witnesses we construct are moreover basis-independent, in the sense that they are invariant under conjugation by local unitaries. Altogether, our results expand the toolbox for entanglement detection in arbitrary local dimensions in a manifestly invariant way.

The Lyth bound asserts that the field excursion of inflaton must be sub-Planckian, thereby imposing an upper bound on the amplitude of the tensor power spectrum in inflationary scenario. This bound is conventionally derived assuming a scale-invariant curvature power spectrum, i.e., $n_s = 1$. However, astrophysical observations confirm a red-tilted spectrum with $n_s < 1$. In light of recent results from the Atacama Cosmology Telescope (ACT) DR6, we revisit these constraints using the newly implied scalar spectral index of $n_s \simeq 0.9743$. Incorporating the ACT data yields a different upper bound on the tensor-to-scalar ratio $r$, which can potentially exclude inflationary scenarios previously robust under the original Lyth bound with $n_s = 1$. Our result highlights the urgent need to combine theoretical Lyth bound considerations with the most up-to-date astrophysical data.

The growth temperature of directly grown boron-compound masks on patterned sapphire can modify the local accessibility of the underlying sapphire surface and thereby alter the subsequent nucleation behavior of GaN. In this work, we investigate how ammonia-borane-derived boron-compound masks grown at different temperatures shape the GaN nucleation landscape within circular SiO$_2$ openings during the initial stage of epitaxial lateral overgrowth. The preferential nucleation position of GaN changes systematically with mask growth temperature: masks grown at 700–750$^\circ$C produce pronounced edge-biased distributions, whereas higher-temperature masks lead to more inward-shifted and spatially sparse GaN domains. Quantitative analysis of the GaN areal fraction, the number of visibly isolated domains, and the radial distribution of domain centers shows that the mask growth temperature affects both the amount of GaN coverage and the spatial arrangement of GaN domains within each opening. The nonmonotonic change in the number of visibly isolated domains is interpreted as a consequence of competition between reduced lateral merging and reduced effective substrate accessibility, rather than as a direct measure of the number of active nucleation sites. Kinetic Monte Carlo simulations reproduce the essential experimental trends by varying the effective density and radial distribution of substrate-accessible sites. These results suggest that the growth temperature of directly formed boron-compound masks provides a practical means of reshaping the intra-opening GaN nucleation landscape by controlling the spatial distribution and effectiveness of local pathways through which GaN precursors can access the underlying sapphire surface.

We compute diffractive structure functions from Wilson line configurations whose energy evolution is given by the JIMWLK equation. We use a JIMWLK evolution setup that has already been constrained with exclusive vector meson production data from HERA. We compare our results to HERA measurements and also extended to heavy nuclei. In particular we can calculate predictions for the nuclear modification factor and diffractive-to-total cross section ratios at the EIC.

Defining magnon topology in strongly frustrated magnets is often hindered by the absence of a simple harmonic magnon vacuum at zero field. Within a classical-spin ground-state search followed by linear spin-wave theory (LSWT), we demonstrate that a representative triangular-lattice K-Gamma-Gamma' model in a dominant-Gamma exchange regime has an in-plane-field-selected compact, noncoplanar seven-site order. This field-selected state provides a controlled classical reference state and hosts magnon bands with field-tunable Chern numbers. Increasing the field drives a Dirac-like band touching that transfers Berry curvature between the fifth and sixth bands, altering the Chern vector from (0, 1, 0, -2, 1, 0, 0) to (0, 1, 0, -2, -1, 2, 0). This topological transition reorganizes the band-resolved thermal Hall conductivity, driving the total $\kappa_{xy}(T)$ through a near-zero crossing once the upper bands are thermally populated. The dynamical structure factor places roughly half of the coherent spectral weight on the Chern-active branches, offering a spectroscopic route to identify the topological branches. These results define a controlled semiclassical benchmark for magnon topology in this pure nearest-neighbor exchange model.

Two-dimensional crystals with densely packed atoms exhibit a range of emerging properties, particularly a wide variety of excitonic behaviors. Thickness-variable layered chromium trihalides with finite surface recombination sites provide an ideal system for understanding how excitons confined in octahedral ligand fields migrate on nanometer length scales, a regime that defies conventional transport probes. In this work, we demonstrate that Cr3+-derived photoluminescence in CrCl3 is spectrally thickness-independent, but its relaxation dynamics are strongly sensitive to thickness and temperature, thereby indicating significant activated migration. A diffusion-coupled surface recombination model reveals an effective out-of-plane diffusivity of 4.5 x 10-6 cm2/s for the ligand-field excitons and a diffusion activation energy of 130 meV. The latter is comparable to the reorganization energy independently estimated from optical Stokes shifts, suggesting that exciton transport is coupled to local lattice relaxation. Furthermore, we show that the relaxation dynamics can be systematically tuned by either enhancing or suppressing surface recombination through controlled surface reactions or encapsulation. This work not only reveals the nanoscopic transport of localized ligand-field excitons but also establishes a spectroscopic transport probe applicable to various 2D materials.

Heavy quarks are produced in the early stages of heavy ion collisions due to their large mass, and subsequently traverse the entire QCD medium evolution. Open heavy flavors provide profound insights into the transport properties of the medium and the process by which quarks neutralize their color charge to form hadrons. In the LHCb experiment, fixed-target collisions cover an unexplored energy range that lies above that of previous fixed-target experiments but below the top RHIC energy for AA collisions. In $p$Pb collisions, heavy quarks are crucial for studying cold nuclear matter effects, which include the modification of nuclear parton distribution functions, energy loss in the nucleus, and other phenomena. These studies provide a baseline for interpreting PbPb measurements.

We develop an analytical framework for coherence-to-entanglement conversion in bipartite high-dimensional quantum systems, so-called qunits. An arbitrary coherent input qunit is coupled to an incoherent ancilla through a generalized controlled-shift operation, producing a maximally correlated bipartite state. By analyzing the partial transpose of the output state, we establish an exact dimension-independent connection between the input coherence and the generated entanglement. We then study how this conversion is affected by three standard noise processes applied after the conversion step: phase damping, global depolarizing noise, and independent amplitude damping. The resulting expressions show that these channels degrade entanglement in qualitatively different ways. Phase damping leads to a uniform attenuation of the entanglement generated from coherence, depolarizing noise introduces pairwise thresholds associated with entanglement sudden death, and amplitude damping produces an asymmetric decay governed by relaxation toward the ground state. For maximally coherent inputs, the general results reduce to simple closed-form behavior, allowing direct comparison of the three noise mechanisms as the system dimension increases. In particular, global depolarizing noise exhibits a dimension-dependent sudden-death threshold, while amplitude damping leads to a smooth suppression in the maximally coherent case. These results provide useful analytical benchmarks for high-dimensional resource conversion and for assessing noisy entanglement generation in qudit-based quantum-information settings.

Transformers perform computations through many successive attention and feedforward blocks, allowing them to learn complex correlations between a large collection of coupled variables. When does stacking successive attention-feedforward computations over many layers provide a computational advantage over a single transformer block? We address this question by examining in-context learning in generalized linear attention transformers. We first introduce a general theory of distributed inference in such transformers, subject to constraints on communication and depth. We show that such systems can exploit internal representations (`function vectors') to infer a latent context variable at increasingly finer scales over its layers. For an in-context linear regression task, the theory predicts that while one-layer transformers without feedforward blocks are optimal for Gaussian priors over the context variable, multi-layer transformers are superior for non-Gaussian, tree-like priors. Trained linear attention transformers reproduce quantitative predictions from the theory. Using causal key-patching experiments, we verify that function vectors in intermediate layers mediate adaptive routing of information. Our results suggest that depth and feedforward blocks enable transformers to implement adaptive inference, and this is advantageous when the distribution over latent variables has hierarchical structure.

The ratio of heavy flavor hadrons is very sensitive to the hadronization mechanism. This proceeding will present recent LHCb results on the cross-section ratios of $D_{s}^{+}/D^{+}$, $\Xi_{c}^{+}/\Lambda_{c}^{+}$ and $\Lambda_{b}^{0}/B^{0}$ in different collision systems. The significantly enhanced production ratios $D_{s}^{+}/D^{+}$ and $\Lambda_{b}^{0}/B^{0}$ with the increase of multiplicity may imply that hadronization mechanisms are modified in high-multiplicity events.

We propose a minimal framework based on a dark $U(1)_D$ gauge symmetry that simultaneously accounts for neutrino masses and dark matter within an inverse seesaw realization. In this setup, the smallness of light neutrino masses is controlled, suppressed by a lepton-number violating parameter $\mu$, which arises dynamically by dark field corrections rather than being introduced by hand. The limit $\mu \to 0$ restores lepton number symmetry, ensuring its, thus neutrino mass, smallness in the sense of 't Hooft naturalness. We analyze the neutrino mass matrix and active-sterile mixing, highlighting their impact on non-unitarity and charged lepton flavor violation. The model is consistent with current experimental constraints while allowing potentially observable signals, such as $\mu \to e \gamma$. The dark $U(1)_D$ symmetry stabilizes the dark matter candidate and links the neutrino and dark sectors. Viable parameter regions satisfying dark matter relic density, direct detection, and collider bounds are identified. This framework provides a minimal and predictive realization of neutrino mass generation and dark matter stability with a naturally small $\mu$ parameter.

We derive and compare three mechanisms of cosmological magnetogenesis: the Thomson-scattering velocity-difference mechanism of Takahashi et al.\ (2005), a new density-gradient source identified here for the first time, and the Harrison bulk-flow mechanism of Cembranos et al.\ (2020). Starting from the coupled Maxwell-Boltzmann equations, the complete kinetic theory chain is derived in a single document – from the BBGKY hierarchy and Thomson collision term, through the generalised Ohm's law, to the second-order magnetic induction equation. The Ohm's law correction terms are each bounded by $m_e/m_p\approx5.4\times10^{-4}$, confirming the standard single-fluid approximation to better than $0.1\%$. At second order in cosmological perturbations, products of first-order scalar source vorticity, we identify a coupling between the photon density contrast $\delta_\gamma \equiv \delta\rho^{(1)}_\gamma / \bar\rho_\gamma$ and the electron-photon velocity difference $(u_e-u_\gamma)^{(1)}$ that was implicitly present in previous treatments but never isolated. Numerical evaluation with CAMB~v1.6.6 at $z=1100$ shows that this term contributes at ${\approx}0.97\times B_{\rm Tak}$, giving a scattering-mechanism total ${\approx}1.4\times$ the Takahashi result. The Harrison mechanism at the Planck bulk-flow limit ($\beta<8.5\times10^{-4}$) yields $B\approx5.7\times10^{-24}$~G at 1~Mpc today and dominates for $\beta\gtrsim2\times10^{-3}$, mildly above the Planck limit. All seed fields exceed the galactic dynamo threshold by many orders of magnitude.

We introduce a mean-field-like computational model for calculating ionization potentials (IPs) based on the pair Coupled Cluster Doubles (pCCD) wave function. Specifically, our model combines the extended Koopmans' theorem (EKT) with the advantages of a variationally orbital-optimized (oo)-pCCD ansatz. The computational cost of the EKT(pCCD) method is negligible (O(N^3)) as the response 1- and 2-particle reduced density matrices used to construct the generalized Fock matrix are readily available after an oo-pCCD calculation. We benchmarked our new computational model for IPs of atoms, small molecules, and a set of organic acceptor molecules against experimental and theoretical reference data. The EKT(pCCD) model significantly improves upon the modified Koopmans' approach [J. Chem. Phys. 162, 184110 (2025)], and the obtained IPs are comparable to those of computationally more expensive IP-EOM-pCCD-based models, approaching CCSD(T) reference values (with a mean error of 0.05 eV). Most importantly, the EKT(pCCD) approach is almost independent of the basis set size, and reliable IPs are already obtained with small basis sets.

We propose a symmetry-resolved optical probe of intrinsic loop-current chirality in moiré materials, with twisted bilayer graphene as a representative realization. Interlayer interference generates chiral electronic circulation on triangular plaquettes, giving rise to an intrinsic geometric chirality that enters the second-order response through a $C_3$-selected angular harmonic of the Berry curvature and can be isolated by the orbital-angular-momentum difference $\Delta\ell$ of interfering optical vortex beams. When moiré $C_3$ symmetry is preserved, the intrinsic contribution appears in the $\Delta\ell=3$ channel of the helicity-dependent dc photocurrent, whereas $C_3$-breaking perturbations activate additional channels. These results establish angular-momentum-resolved nonlinear optics as a route to probing geometric chirality in moiré and other symmetry-engineered quantum materials.

The hyperbolic mode (HM) refers to a polariton mode in a polar insulator where the dielectric function is negative in some direction of propagation. Within a frequency window the light occupies a greatly expanded region in momentum space. The HM in hexagonal Boron Nitride (hBN) has been under intense study and we consider placing a metal directly on top of hBN and ask whether its physical properties can be strongly affected. While the problem resembles superficially the electron phonon coupling problem, there are important differences. Due to the longitudinal nature of the HM mode the coupling is driven by time dependent charge fluctuations which results in a coupling that strongly increases with the energy difference of the initial and final states. We find a significant frequency and momentum dependence of the self energy which allows us to identify the dimensionless coupling constant $\lambda_0$ that controls this effect. There is a suppression of the quasi-particle weight but it turns out that the leading correction to the velocity renormalization is canceled. We compute the single particle spectral function which shows a side band that can be measured experimentally. The virtual exchange of HM leads to a repulsive interaction which is ineffective to leading order because of the energy dependence. We are motivated to seek pairing by going to second order. Unfortunately we find that the leading contributions exactly cancel. This cancellation is not an accident and we give an explanation of why this cancellation would take place.

The hyperbolic mode (HM) refers to a polariton mode where the dielectric function is negative in some direction of propagation. Within a frequency window the light occupies a greatly expanded region in momentum space. We compute the photon density of states and find that the zero point fluctuation in the RMS electric field can reach $MV/cm$, comparable to the largest field used in pump probe experiments in the THz scale. The HM in hexagonal Boron Nitride (hBN) has been under intense study and we consider placing a material directly on top of or sandwiched between hBN crystals. We consider two examples. First the material is a metal and we calculate the modification of the quasi-particle spectral weight, Fermi velocity and pairing interaction. Next we consider a material that is close to the Mott transition. We find that a substantial shift in the metal-insulator transition is possible, but the effect decays rapidly with distance, so that only a few monolayers are affected. We provide estimates and suggestions for a number of materials of interest.

We study non-minuscule boundary 't Hooft lines in four-dimensional $\mathcal N=4$ $U(N)$ super Yang–Mills theory with the regular Nahm-pole boundary condition. For one-row charges we construct the exact spherical-DAHA operator $\mathbf e_+h_r(Y)\mathbf e_+$, determine its finite shift expansion and discrete Macdonald spectrum, and evaluate the S-dual Neumann Wilson two-line index as a finite-$N$ Macdonald pairing. For the first non-minuscule $U(2)$ coefficient, a local two-minuscule convolution model with Higgs branch $T^*\mathbb P^1$ has two Jeffrey–Kirwan residues, while subtracting the determinant intersection-cohomology summand supplies the additional $-\mathfrak t$ term. The same transverse $A_1$ calculation, dressed by the spectator-root factor, reproduces the first lower $U(3)$ coefficient. The local convolution calculation and its spectator lift provide low-rank checks of the complete DAHA coefficients independent of the inverse recursion, while their boundary-localization interpretation remains conjectural. Assuming an isometric oriented boundary Fourier intertwiner, the DAHA construction is compatible with the expected boundary S-duality relation.