Papers

We introduce the lattice quark potential model (LQPM), which discretizes the nonrelativistic quark potential model on a periodic cubic lattice and diagonalizes the resulting many-body Hamiltonian exactly. Unlike variational approaches, which provide only upper bounds on the energy, LQPM removes this variational bias, and its remaining finite-volume uncertainty is removed by extrapolation. Formulated directly in coordinate space, the method is indifferent to the specific form of the potential and accommodates arbitrary interactions, such as including three-body forces and spin-orbit and tensor couplings, that are difficult to treat in conventional few-body approaches. As a benchmark, the charmonium and $\Omega_{ccc}$ spectra are reproduced within a few MeV of experiment. For the fully charmed tetraquark $cc\bar{c}\bar{c}$, we obtain a $J^P=0^+$ ground state at $5934.8(13)~\mathrm{MeV}$, $33.2(13)~\mathrm{MeV}$ below the $\eta_c\eta_c$ threshold, unambiguously identified as a deeply bound tetraquark whose existence is robust against the choice of potential. Such a state can decay into two dileption pairs $2(e^+e^-)$ via $J/\psi e^+e^-$, with significance similar to $X(6400)$, or about one order of magnitude smaller. Lying below the lowest strong-decay channel, it can decay only through electromagnetic and weak interactions. Our results establish exact lattice diagonalization as a controlled, systematically improvable, and broadly applicable route to multiquark spectroscopy, providing a quantitative benchmark for the strong interaction and valuable guidance for future experimental searches for exotic hadrons.

We show that in hot QCD rotating at an imaginary angular velocity $\Omega_I$, the angular velocity selects not only the temperature of the bulk but whether charge conjugation $C$ is broken there. For QCD at temperature $T$ and imaginary quark chemical potential $\theta$, with $\Omega_I/2\pi=p/q$ in lowest terms, the bulk far from the rotation axis is in the same thermal equilibrium state as nonrotating QCD at temperature $T/q$ and imaginary quark chemical potential $\theta'=q\theta+\pi(p+q+1)$; this follows from the Euclidean boundary conditions and locality alone, and holds nonperturbatively. Consequently, even at zero quark chemical potential, the bulk is placed at the Roberge-Weiss (RW) point whenever $p$ and $q$ are both odd, and $C$ is spontaneously broken there for $T>qT_{\rm RW}$, with $T_{\rm RW}$ the RW endpoint temperature. The bulks at $\Omega_I=2\pi/3$ and $4\pi/3$, for example, are both at temperature $T/3$, yet only the former can break $C$. The set of imaginary angular velocities at which $C$ is broken has a fractal structure: raising $T$ adds rationals of ever larger denominator. At irrational $\Omega_I/2\pi$ the bulk corresponds to zero-temperature QCD at any $T$ and remains confined.

A fermion mass pairs a field with a partner of conjugate charge: elementary (Higgs-Dirac), self-conjugate (seesaw) or a three-fermion composite (symmetric mass generation, SMG). We give half of a Spin(10)-like generation an explicit Majorana mass in a four-dimensional SMG model and ask what the other half does in a phase with no condensate. With the source on, every mass-type term of the unsourced half averages to zero under the symmetry group of the sourced action, so a light mass term, and a seesaw's light-heavy mixing, requires a spontaneously broken symmetry; exact on the lattice and a general proposition. The source is colour-democratic (a Delta_R-type mass on every flavour's right-handed taste doublet); the single-nu_R split lies outside the positivity class used but inside the symmetry statement. Measured up to 8^4: (i) in the symmetric-gap phase, with the source screened to at most 1.1% of free, the unsourced half's single-fermion readout stays at 0.3% of free while its pair susceptibility rises from 0.2% to 1.2-1.7% at h=2; on like mode sets it falls with the volume, on (4^4,8^4) no inequivalent light mass channel grows faster than free, and symmetry breaking is not resolved at L<=8; (ii) at the critical point the explicit mass collapses the critical sigma channel and moves the light half toward free as a saturating crossover, not a power law; direction tests (MIXED by their pre-registered letter) are consistent with a critical coupling rising with the mass; y_c(h) is not located. Pole versus zero of the light propagator at p->0 is not measured. The outcomes are readings after pre-registered tests that mostly returned no verdict. Also: no first-order signature of the merged transition at L<=8, a Z_4-odd response handed to a lattice composite, and flavour democracy of the positivity class. Every claim has an evidence class and a runnable check.

Continuum Schwinger function methods\linebreak (CSM) are used to provide estimates of pseudoscalar meson pole contributions - $\mathsf P = \pi^0$, $\eta$, $\eta^\prime$, $\eta_c$, $\eta_b$ - to the muon anomalous magnetic moment. The analysis framework is benchmarked via successful applications to an array of other meson and nucleon properties. It uses the leading order CSM truncation, augmented by a parametrisation of non-Abelian anomaly effects, to deliver an internally consistent treatment of all the pseudoscalar–two-photon transition form factors required to complete such a calculation. Employing those form factor predictions, the following results are obtained (units $10^{-11}$): $a_\mu^{\pi^0} + a_\mu^{\eta} + a_\mu^{\eta^\prime} = 84.3(0.8)$ - a value lower than some other contemporary estimates; $a_\mu^{\eta_c} = 0.82(0.04)$; and a value of $a_\mu^{\eta_b}$ that is negligible. The total contribution is $\sum _{\mathsf P} a_\mu^{\mathsf P} = 85.1(0.8) / 10^{11}$. Our analysis suggests that this pole contribution to $a_\mu$ is still not known with precision better than 5%.

We discuss some recent applications of the Born-Oppenheimer effective field theory (BOEFT) formalism, directly derived from QCD and grounded in scale separation and symmetries, to hadronic systems containing two heavy quarks. This formalism provides a unified description of both ordinary and exotic quarkonium states (i.e., hybrids, tetraquarks, pentaquarks, ...) dynamics via coupled Schrödinger equations, whose potentials are computable on the lattice. The aim is to unveil the elusive pattern of the XYZ exotic hadrons. Here, we apply the BOEFT formalism to the $\chi_{c1}(3872)$, $T_{cc}(3875)^+$, and their bottom counterparts. Moreover, we assess the threshold effects on the quarkonium spectrum and discuss the inclusive production cross section for $\chi_{c1}(3872)$.

In view of the recent experimental finding of the heavy quark flavor partner of the $D_{s0}(2317)$ in the bottom sector, the $B_{s0}(5700)$, we perform the $B^{(*)}\bar{K}^{(*)}$ coupled-channel calculation in the hidden-gauge formalism. By fixing the mass of the bound state generated by the $B\bar{K}$ interaction with $J^P=0^+$ to the observed state, we also predict five new states with $J^P=\lbrace 0,1,2\rbrace^+$ in this sector. In particular, three of them have $J^P=1^+$ and masses $5740$, $6005$ and $6065$ MeV, respectively. In addition, we evaluate the decay width of the $B_{s0}$ and $B_{s1}$ states through the isospin breaking decay mode $B_s^0\pi^0$ and $B_s^{*0}\pi^0$, respectively. We find that, because these states have large binding energies with respect to the $B^{(*)}\bar{K}$ threshold, the coupling to the bare component can reduce this decay width by more than half of the decay width, from $50$ keV in the purely molecular model to $10-20$ keV, when the $B_{s0}$ is coupled to the bare component. We also observe that, after considering heavy-quark-spin violating contributions, the decay width for the $B_{s1}$ becomes smaller than for the $B_{s0}$.

The measure of indirect CP violation in the neutral kaon system, $\epsilon_K$, is an important precision test of the Standard Model. A first-principles Standard Model prediction of $\epsilon_K$ requires evaluating the long-distance contribution in which the $\Delta S = 2$ process proceeds via two $\Delta S = 1$ operators. The non-perturbative nature of QCD in the relevant energy regimes requires a lattice QCD simulation. In this paper we present the two-loop, $O(\alpha_s)$ RI/SMOM - $\overline{\text{MS}}$ matching factors required to renormalize a lattice QCD calculation of the long-distance contribution to $\epsilon_K$.

We present a phenomenological study of the longitudinal unpolarized structure function $F_{UU,L}$ in semi-inclusive deep inelastic scattering (SIDIS) and its ratio with the transverse structure function, $R_{\, \rm SIDIS}=F_{UU,L}/F_{UU,T}$. We study their transverse-momentum dependence, combining for the first time low- and high-transverse-momentum contributions across the kinematic range relevant to SIDIS measurements. At low transverse momentum, $F_{UU,L}$ is power suppressed, making it sensitive to next-to-next-to-leading-power dynamics in the unpolarized sector. We find that this contribution can be sizable, with $R_{\, \rm SIDIS}\simeq 0.3$ at low transverse momentum and hard scale, producing a correction of the order of $10\%$ to transverse-momentum-integrated observables. Although these estimates remain subject to theoretical uncertainties, our results indicate that accounting for $F_{UU,L}$ is likely to be important for the interpretation of SIDIS multiplicities and motivate dedicated measurements of $R_{\, \rm SIDIS}$ to better constrain the longitudinal contribution.

The hopping expansion is an important approximation of the quark propagator in lattice quantum chromodynamics, but it diverges for light quarks, which limits the scope of strong-coupling and finite-density simulations. We present an artificial scientific discovery framework using gauge-equivariant neural networks in the Clifford basis to extract interpretable approximations. Our approach yields improved low-order approximations that outperform the hopping expansion at identical computational cost. In the parameter regime where the hopping expansion fails, our approach identifies convergent behavior, thus suggesting a novel series expansion. The discovered approximations generalize to unseen gauge fields and volumes, enabling immediate implementation as plug-in replacements and a new theoretical understanding of quark-propagator expansions.

Gauge theories describe fundamental interactions in the standard model of particle physics and build effective theories in condensed matter physics. Being notoriously hard to simulate, these theories are commonly regularized as lattice gauge theories which can be evaluated with high precision through Monte Carlo algorithms or variational methods. However, Monte Carlo algorithms are not applicable in all regimes due to the sign problem; while variational methods, quantum and classical alike, only give upper-bounds on the ground-state energy. Their precision crucially depends on the chosen ansatz. Here, we present a framework based on a hierarchy of semidefinite programs to yield increasingly good lower-bounds on the ground-state energy and propagate these bounds to extended observables like Wilson loops and mesonic strings. We demonstrate the numerical capabilities by applying the algorithm to a (1+1)-dimensional $\mathbb{Z}_2$ theory with dynamic fermionic matter and its pure-gauge version in (2+1)-dimensions. In both cases, we obtain certified intervals for the ground-state energy. For a one-dimensional system with 129 sites, the certified interval has a relative spread of $0.04\%$. For a two-dimensional system with 97 sites (corresponding to a $7 \times 8$ lattice), the relative spread is $2.08\%$. Beyond energy estimates, the proposed method provides rigorous bounds on both short- and long-range observables such as Wilson loops over multiple plaquettes and the magnitude of the mesonic string. The method can be both used as a computational microscope into many-body physics and a way to certify results of quantum simulators.

Hadron resonances are intrinsically dynamical states whose observable properties are governed by the interplay between quark-model configurations and hadronic channels. Hamiltonian effective field theory provides a practical framework for connecting hadron dynamics with experimental observables and lattice QCD results. In this review, we outline the infinite- and finite-volume formulations of Hamiltonian effective field theory and survey its applications to light-hadron spectroscopy and resonance structure. By constraining the same Hamiltonian framework with experimental scattering data and lattice QCD spectra, Hamiltonian effective field theory can help distinguish among scenarios that describe the available scattering data comparably well but imply different roles for bare-state and multihadron configurations. We also review recent extensions of the Hamiltonian framework developed to address more complicated dynamical settings.

Linear radiation transport equations (RTEs) form the simulation foundations underpinning design and analysis tasks in nuclear engineering, inertial confinement fusion, medical imaging, and astrophysics, but resolving the high-dimensional phase space at engineering fidelity remains expensive enough that outer-loop workflows, such as design optimization, uncertainty quantification, and parameter sweeps, are routinely budget-bound on traditional solvers. Neural surrogates promise to relax this bottleneck by amortizing simulation cost across thousands of downstream queries, but the architectural choices and engineered inductive biases that make a surrogate accurate on one transport problem do not transfer straightforwardly across model families. We benchmark two parameter-matched neural surrogate architectures, the physics-attention Transolver and the multi-scale graph network Bi-Stride Multi-Scale MeshGraphNet (BSMS-MGN), as end-to-end approximations of the final-time particle concentration for the two-dimensional linear RTE on the canonical Lattice and Hohlraum benchmarks. An ablation across Fourier features and region-weighted training loss exposes strongly architecture-dependent inductive-bias preferences, indicating that design choices common to physics-informed surrogate workflows must be revisited per architecture rather than imported across model families, and that downstream utility depends on per-QoI sensitivity rather than a single field-level score. The model training recipe, training data, and evaluation pipeline are released alongside this paper to support reproduction, transfer to related transport problems, and evaluation as amortized forward-model components in larger outer-loop simulation workflows.

We demonstrate that form factors evaluated at complex-valued momenta can be directly accessed from position-space Euclidean correlators without analytically continuing the latter and without solving an inverse problem. The approach directly applies a bilateral Laplace transform to the lattice data, which provides the analytically continued form factor wherever it converges. Focusing on the pion form factor in Quantum Chromodynamics (QCD), this gives access to the observable as a function of invariant \(Q^2\) throughout an extended analytic domain consisting of all complex \(Q^2\) with real part larger than \(-4m_\pi^2\). This could, for example, be used to improve charge-radius determinations or provide more complete data for fits based on conformal mapping of the data. After developing the approach for infinite-volume correlators, we discuss various options for finite-volume estimators suitable for realistic calculations, including position-space fits or application of a spatial chemical potential represented by boundary conditions with an imaginary twist angle. Finally, we test the method in the two-dimensional \(O(3)\) nonlinear sigma model using Monte Carlo data.

We investigate the impact of radiative corrections on the ratio of the semileptonic decay rates $\Sigma^\pm\to\Lambda e^\pm \bar{\nu}$. Phenomenological analyses point to sizable radiative effects on the experimentally measured ratio. From a theoretical perspective, this observable is particularly appealing because several hadronic and electroweak contributions partially cancel in the ratio, providing a cleaner probe of electromagnetic effects. We identify the dominant contributions to the radiative corrections and develop the framework for a dedicated calculation. This represents a first step toward a precise theoretical description of baryon semileptonic decays, helping to assess their potential as precision tests of the Standard Model.

We consider the $\phi^4$ theory with $\phi(x)\in\mathbb{R}$ in three Euclidean dimensions. For a variety of self-couplings $\hat{\lambda}$, the critical (bare) parameter $\hat{\mu}_{0\mathrm{c}}^2(\hat{\lambda})$ is determined where the lattice-regulated system changes from the symmetric phase to the broken phase. Next, we send the box volume to infinity and switch to a universal scheme; this yields $\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$ for each simulated $\hat{\lambda}$. Finally, a continuum extrapolation gives $f_\mathrm{c}=\lim_{\hat{\lambda}\to0} \hat{\lambda}^2/\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$, and we find $f_\mathrm{c} = 18.808(64)_{\mathrm{stat}}(45)_{\mathrm{sys}} = 18.808(78)_{\mathrm{tot}}$. In addition, $\Delta\langle\phi^2\rangle_\mathrm{c}/\lambda = -0.00303(12)_{\mathrm{stat}}(12)_{\mathrm{sys}} = -0.00303(17)_{\mathrm{tot}}$ is determined in the combined continuum and infinite-volume limit.

The internal structure of hadrons is governed by nonperturbative Quantum Chromodynamics (QCD). This dissertation presents first-principles calculations of partonic observables using lattice QCD and effective field theory, with controlled systematic uncertainties, advancing from collinear structure to transverse-momentum-dependent distributions (TMDs) that encode the three-dimensional partonic structure of hadrons. Within the large momentum effective theory (LaMET) framework, this work presents state-of-the-art calculations of pion distribution amplitudes and systematic studies of nucleon parton distributions, with control of renormalization, excited-state contamination, Fourier-transform systematics, and power corrections. A Coulomb-gauge formulation of quasi-distributions simplifies ultraviolet structure by avoiding Wilson-line related linear divergences, with Gribov-copy effects found to be negligible at current statistical precision. Building on these developments, this dissertation reports lattice determinations of nucleon TMD parton distributions, the Collins-Soper kernel, the intrinsic soft function, and pion TMD observables. These results provide nonperturbative inputs for global QCD analyses and the precision hadron-structure program, including the Electron-Ion Collider. In parallel, this work explores machine-learning acceleration of lattice gauge simulations through neural field transformations embedded in Hybrid Monte Carlo. In two-dimensional U(1) tests, the method reduces autocorrelation and improves performance toward finer lattice spacing, suggesting potential applications to more efficient lattice QCD simulations.

We apply the stochastic all-mode technique to general coarse-graining schemes of the tensor renormalization group (TRG) approach. The technique possesses a notable characteristic of being entirely free from systematic errors which can potentially arise in the coarse-graining step, while it has statistical errors caused by random noise. The key element in our generalization is employing a method called squeezer, and the all-mode technique can be used when it is constructed. Since many TRG methods can be described in terms of the squeezers, our approach can be applicable in all such cases. In this work, we demonstrate the new method with higher-order TRG in the two- and three-dimensional Ising model.

We develop a finite element method (FEM) for partial differential equation (PDE) solver based on the entanglement-basis representation introduced in our companion work. By lifting non-linear finite-element equations into an augmented coefficient space, the governing PDE together with boundary, initial, and inter-element constraints can be expressed through a unified quadratic residual minimization. Although this augmented space grows exponentially with the number of elements, its tensor-product structure allows it to be represented efficiently using tensor networks. Using the matrix product state (MPS) as a concrete example, we show that density matrix renormalization group (DMRG) sweeps enable element-by-element optimization without explicitly constructing the full augmented space. For bounded bond dimension, the resulting computational cost scales polynomially with the number of finite elements. We extend the framework to time-dependent problems through implicit temporal discretization and demonstrate convergence under both mesh and polynomial refinement using diffusion equations.

We study the thermodynamics of the BMN matrix model at large $N$ and strong coupling, using its dual black holes in eleven-dimensional supergravity. Within the consistent truncation to two-dimensional $SO(9)$ gauged supergravity, the static $SO(3)\times SO(6)$-invariant black holes solve ordinary differential equations, which we solve to high precision. We formulate holographic renormalisation for this truncation and fix the finite counterterms using a supersymmetric solution. This gives the energy, the entropy and the response to the BMN mass independently, and we verify the first law and the Smarr relation along the branch. The thermal branch ends at a critical value of $\mu/T$, which power-law fits place at $4\pi$ with an estimated uncertainty below $10^{-10}$. The first-order transition inferred in earlier work, where the free energy was reconstructed from the entropy, does not survive, and an independent eleven-dimensional calculation agrees with ours over the range it covers. Instead, the free energy, the entropy and the mass response approach their values in the confined phase continuously at the end of the branch, where the solutions become singular. If this branch remains the dominant one up to its end point, the transition therefore coincides with the singularity. Near the end of the branch, the scalar fields follow a solution of the supersymmetric first-order equations, while the metric carries a nontrivial blackening factor. The horizon develops a neck whose profile is universal, with radii growing as the $2/5$ power of the distance from the pinch. Within the range we resolve, the geometry is not that of the Ricci-flat double cone which governs mergers of vacuum black holes.

We present a technique for computing Drell-Yan lepton pair production at particle-level that achieves N$^3$LO and approximate N$^4$LL$'$ accuracy at small to moderate transverse momentum, tree-level precision for $Z+4$, $5$, and $6$ jets, and approximate NLO EW precision at high transverse momentum. A crucial non-perturbative input, the Collins-Soper kernel, is obtained from continuum-limit lattice QCD results. High-precision theory results are recast into strictly positive event weights using an information-theoretic approach based on the maximum entropy principle.

We develop a gauge-invariant effective field theory for scalar glueball interactions based on the Yang-Mills gluon condensate. Starting from a coherent-state formulation of the Yang-Mills vacuum, we derive an effective Lagrangian for the scalar glueball and its interactions with gluons. The resulting crossing-symmetric amputated four-gluon Green's function is projected onto the color-singlet $J^{PC}=0^{++}$ channel, yielding a normalized scalar glueball form factor that factorizes into universal kinematic structures and an intrinsic glueball function. The formalism predicts a parameter-free effective interaction radius for the ground-state scalar glueball with resonance $f_0(1710)$, $r_{\rm int}=\sqrt{6}/m_\phi=0.28$ fm, which is in excellent agreement with recent lattice Yang-Mills determinations of the mass-radius ($r=0.263(31)$ fm). The predicted momentum dependence of the normalized form factor is consistent with lattice Yang-Mills gravitational form factor data, with the $f_0(1710)$ candidate providing the best overall fit and $r_{\rm int}$. Inclusion of the first excited $0^{++}$ glueball produces modest corrections to the interaction radius ($r_{\rm int}^*=0.240$ fm) while yielding stable and kinematically robust modifications of the form factor. This framework provides a systematic bridge between effective field theory and first-principles lattice Yang-Mills calculations of scalar glueball dynamics.

Thermal axion production in the early Universe is controlled by the QCD topological-charge-density spectral function evaluated on the light-cone as a function of momentum k. We show how weighted integrals of this quantity can be computed using Euclidean lattice QCD without any analytic continuation, similar to what Harvey Meyer and collaborators have recently done for the photon production rate. We then test the approach in pure-glue QCD at T=1.5 Tc, finding that it is feasible to extract at least one and possibly two finite weighted k-integrals of the k-dependent production rate. This opens the possibility for extractions in full QCD at temperatures around and somewhat above the crossover temperature, where other methods are not reliable.

We investigate the gravitational $D$-form factors of the nucleon and pion within an extended linear sigma model (eLSM) that incorporates both two-quark and four-quark states, as well as nucleon fields. Within the scalar-meson-dominance picture, we find that meson mixing between two-quark and four-quark states suppresses the nucleon $D$-form factor and leads to agreement with the lattice-QCD results. Interestingly, a quantitatively similar suppression was previously found in the parity doublet model (PDM) as a consequence of a nonzero chiral invariant component of the nucleon mass. This suggests that the effects of meson mixing and the chiral invariant mass are difficult to distinguish from the nucleon $D$-form factor alone. We therefore examine the pion $D$-form factor in the chiral limit. While its value in the forward limit remains fixed at $-1$ in both the eLSM and the PDM, meson mixing modifies its momentum-transfer dependence. In contrast, the chiral invariant mass does not directly affect the pion $D$-form factor. These results suggest that a combined analysis of the nucleon and pion $D$-form factors can provide further insight into the mass decomposition of the nucleon and the quark composition of mesons.

Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.

Using fractional anomalous determinants, we construct a model of the trace and axial anomalies of a $SU(3)$ gauge theory at nonzero $\theta$ angle through the couplings to scalar and pseudoscalar glueballs. In the pure gauge theory, we reproduce the $\theta$ dependence of the vacuum energy and the scalar-glueball mass from the lattice, and estimate the jump in the topological charge density for the first-order transition at $\theta = \pi$. In QCD, the coupling of a pseudoscalar glueball to fractional anomalous determinants describes all of the four three-pseudoscalar decay channels of the $0^{-+}$ glueball candidate $X(2370)$ measured by the BESIII collaboration. Measuring the decay rates for $\eta \eta \eta$ and $\eta \eta \eta'$ can provide a stringent test of the model.

At high temperature instantons form a dilute gas, so in QCD-like theories the breaking of the anomalous $U(1)_A$ symmetry is given by integral powers of the anomalous determinant, $\sim (\det \Phi)^{Q}$, where $\Phi\sim \overline{q}_L q_R$ is bilinear in the quark fields, and with untwisted boundary conditions, the topological charge, $Q$, is an integer. A syncretic model is constructed, which is manifestly "beyond Landau". In the chiral limit, at temperatures above the chiral phase transition, $T > T_\chi$, only integral powers of the anomalous determinant appear. Below $T_\chi$, following 't Hooft et al. I assume that the topological charge $Q$ is fractional, as an integer times $1/N_c$, where $N_c$ is the number of colors. I suggest that consequently, fractional powers of the anomalous determinant appear in the chiral effective Lagrangian. For $N_f$ degenerate flavors, this generalizes the Witten-Veneziano term, valid for small $N_f/N_c$, to arbitrary $N_f/N_c$. In this model the chiral phase transition is generically of second order. The two exceptions are for one flavor, where it is probably crossover, and three flavors, where it could well be weakly first order. This can be tested in lattice QCD with $2+1$ flavors by comparing the (known) temperature dependence of the difference of the $\pi^a$ and $a_0^a$ propagators, to the chiral condensate of the strange quark, between $T_\chi$ and $\sim 2 \, T_\chi$. Analogous measurements are possible for one to four degenerate flavors about $T_\chi$. Lastly, I propose an operator for baryon number in the symmetric phase.

We compute one-loop unpolarized quark and gluon quasi- and pseudo-distributions in $\overline{\mathrm{MS}}$ and match them to light-cone PDFs. Decomposing the gluon correlator into six covariant form factors, we derive the $6\times6$ renormalization mixing matrix: its eigenvectors classify multiplicatively renormalizable combinations, and any lattice operator choice projects onto our results without a further loop calculation. Evaluating all Fourier transforms in $d$ dimensions, we resolve the structure of the exterior $|x|>1$ in quasi-distributions. The correlator carries a short-distance logarithm with a branch cut at $\nu=0$. By the Paley-Wiener theorem, the analytic part transforms into $|x|\le1$, so the exterior is generated solely by this branch cut. At leading power, the exterior carries no independent non-perturbative physics: it is fixed by the light-cone PDF through the renormalization group. In LaMET, lattice data therefore cannot determine the exterior independently of the interior, and unconstrained exterior parameters in reconstructions risk absorbing genuine power corrections into the leading-twist PDF. In the gluon channel, the matching kernel of Balitsky, Morris and Radyushkin differs from our $\overline{\mathrm{MS}}$ result by a finite polynomial, identical across index choices. We trace this to contracting an internal loop index over two instead of $d-2$ transverse directions, omitting an evanescent operator on the collinear pole. Using our basis, we show that the independent kernel of Yao, Ji and Zhang agrees with ours, separated from Balitsky et al. by the same polynomial. While the ratio scheme protects the momentum fraction $\langle x\rangle_g$, this kernel difference suppresses the extracted normalized second and third gluon moments by $11\%$ and $13\%$ at $\alpha_s=0.3$, so the true $\overline{\mathrm{MS}}$ gluon is systematically harder than reported.

Gauss constraints make it nontrivial to open, close or join a gauge system while retaining its interior physics. Boundary reconstructions are constructed on a pure SU(3) ladder at six site-singlet cutoffs, with all allowed intertwiner multiplicities. Replacements of prescribed length are obtained using legal column paths and physical self-loops. On their stated physical domains, the channels preserve unnormalized conditional interior matrices, including their weights and within-branch coherence. Lowest-cutoff dephasing controls show that path probabilities alone do not preserve the matched magnetic observables. In that example, coherent resources lower the output energy without purification or global ground-state preparation. Matched interior Hamiltonian terms cancel exactly, so the energy cost is bounded independently of longitudinal length. The vacuum and flux energy densities are then established separately by same-sector gluing and stability. The open and periodic vacuum-subtracted line-energy densities are shown to be equal by two same-length boundary comparisons using the qualified periodic minimizing domain. These limits hold at fixed lattice spacing, transverse width, coupling and chosen cutoff.

Hamiltonian simulations of lattice gauge theories promise new insights into the inner workings of QCD. The rapid development of quantum computing hardware suggests that large scale simulations may soon become feasible. However, no efficient formulation suitable for simulations near the continuum limit is currently known for the non-Abelian case, and existing candidates typically feature long range interactions in the electric part of the Hamiltonian. We prove that such non- localities are unavoidable when the gauge configuration is reparametrised while preserving both the number of degrees of freedom and the fundamental commutation relations. We then attempt to mitigate this by introducing additional gauge links alongside additional constraints. Although this approach is successful in U(1), we prove that the corresponding construction is inconsistent for non-Abelian lattice gauge theories.

We study superfluid vortices in two-color QCD and more general pseudoreal gauge theories with even flavor number $N_f=2m$ at finite baryon density. The antisymmetric diquark condensate admits fractional minimal vortices with baryon-phase winding $\nu=1/m$, corresponding to $1/m$ of the conventional circulation quantum, each localizing an $Sp(2)\simeq SU(2)$ core sector. For vortices embedded in mutually orthogonal flavor planes, the leading-order chiral action factorizes exactly. Off-diagonal flavor zero modes are non-normalizable at finite separation but become localized at coincidence, enhancing the normalizable sector from $[Sp(2)]^m$ to $Sp(2m)$. For fundamental fermions of an $Sp(2N)$ gauge theory, the bulk Wess–Zumino–Witten (WZW) term descends compatibly: a cluster of $n$ coincident minimal vortices carries an $Sp(2n)_N$ WZW theory, while a flavor-symmetric vortex with positive integer baryon-phase winding $\nu$ carries $Sp(2m)_{N\nu}$. At unit winding this yields the vortex map to $Sp(2m)_N$, with central charge $c=Nm(2m+1)/(N+m+1)$ at the WZW fixed point, and suggests a broader nonsupersymmetric four-dimensional/two-dimensional correspondence.