We apply score-based diffusion models to two-dimensional SU(2) lattice pure gauge theory with the Wilson action, extending recent work on U(1) gauge theories. The SU(2) manifold structure is handled through a quaternion parameterization. The model is trained on 10,000 configurations generated via Hybrid Monte Carlo at a fixed coupling $\beta_0= 2.0$ on an $8\times 8$ lattice, augmented to 20,000 samples via random gauge transformations. Through physics-conditioned sampling exploiting the linear $\beta$-dependence of the score function, we generate configurations at different values of the coupling without retraining; through the fully convolutional U-Net architecture with periodic boundary conditions, we generate configurations on lattices of different spatial extents. We validate our approach by comparing the average plaquette and Wilson action density against exact analytical predictions. At the training lattice size ($8\times 8$), the model reproduces the exact plaquette with biases $|\Delta| \leq 0.001$ for $\beta \in [1.5, 2.5]$ and $|\Delta| < 0.06$ across $\beta \in [1, 4]$. For lattices sharing the training extent $L=8$ in at least one direction, biases remain below $\sim 0.003$ for $\beta \in [1.5, 2.5]$, with larger deviations at higher couplings. This work demonstrates that diffusion models are a promising tool for non-Abelian gauge field generation and motivates further investigation toward higher-dimensional theories.

In this paper we produce evidence that confinement of colour is due to dual superconductivity of $QCD$ vacuum. To do that we put together results of old numerical simulations and results of more recent investigations. The starting point is the expectation that gauge theories admit a dual description in terms of monopoles. The strategy is then to construct the creation operator $\mu$ of a monopole and to compute its vacuum expectation value $\langle \mu \rangle$ , the disorder parameter which indicates dual superconductivity. The Imechanism of confinement is dual superconductivity of vacuum if $\langle \mu \rangle \neq 0 $ in the confined phase , and $\langle \mu \rangle =0$ in the deconfined phase. Confinement has to be certified by independent methods. It is shown that gauge invariance requires that field strengths be replaced by gauge invariant field strengths, which are their parallel transports to infinity. The resulting disorder parameter is a sum of correlation functions of gauge invariant field strength, and its behaviour understood by use of existing lattice data of two-point gauge invariant correlations. As a byproduct an apparent existing inconsistency, the lack of preferred orientation in colour space of the chromo-electric field inside confining flux tubes, is resolved.

We study near-threshold $D\bar{D}$ scattering in $S$ and $D$-wave to determine whether or not resonances or bound states are present. Working in the approximation where charm-annihilation is forbidden, with two degenerate light-quark flavors and a heavier strange quark, isospin is a good quantum number, and the only other other channel that is kinematically open is $\eta_c\eta$. Using lattice QCD we compute, as a function of varying light-quark mass, the $S$-matrix for coupled-channel $\eta_c\eta - D\bar{D}$ scattering and find only weakly interacting meson pairs. In contrast to several other studies, we find no evidence for any bound-state or resonance singularity in the energy region between the deeply-bound $\chi_{c0}(1P)$ state and the $D_s\bar{D}_s$ threshold.

We introduce a novel observable associated to Abelian monopole currents defined in the Maximal Abelian Projection of SU(3) Yang-Mills theory that captures the topology of the current loop. This observable, referred to as the $\textit{simplicity}$, is defined as the ratio of the zeroth over the first Betti number of the current graph for a given field configuration. A numerical study of the expectation value of the simplicity performed in the framework of Lattice Gauge Theories enables us to determine the deconfinement temperature to a higher degree of accuracy than that reached by conventional methods at a comparable computational effort. Our results suggest that Abelian current loops are strongly correlated with the degrees of freedoms of the theory that determine confinement. Our investigation opens new perspectives for the definition of an order parameter for deconfinement in Quantum Chromodynamics able to expose the potentially rich phase structure of the theory.

The ability to engineer topologically distinct materials opens the possibility of enabling novel phenomena in low-dimensional nano-systems, as well as manufacturing novel quantum devices. One of the simplest examples, the SSH model with both even and odd number of sites, demonstrates the connection between localized edge states and the topology of the system. We show that the SSH model hosts localized spin centers due to the interplay between the localized edge states and the on-site Hubbard interaction. We further show how one can engineer any number of localized spin centers within the chain by careful addition of defects. These spin centers are paired in spin-singlet or spin-triplet channels within each block separated by the defects, and together they construct an array of spin singlet and/or triplet qubits. As this system is realizable experimentally, our findings describe a novel way for manipulating and engineering spin qubits and therefore provide a platform for performing many-body quantum simulations on spin excitations like magnons and triplons.

Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random matrices. This limit corresponds to a fixed point of a pregeometric Renormalization Group flow in which the tensor size $N$ serves as the Renormalization Group scale. We search for corresponding fixed points in order-4 random tensor models associated to dynamical triangulations in 4 dimensions. In a $O(N)^{\otimes 4}$ symmetric setting, we discuss the resulting phase portrait as a function of the regulator parameters. We optimize our results, identifying parameter values for which the results are minimally sensitive to parameter changes. We find three fixed-point candidates: only one of them is real across the entire parameter range, but only has two relevant directions. This should be contrasted with the university class of the Reuter fixed point in continuum quantum gravity, very likely characterized by three relevant directions. We conclude that simple combinatorial models of Euclidean triangulations and the Reuter fixed point most likely lie in different universality classes.

Tensor states $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}}=\Upsilon B_{c}^{\ast -}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{c}}=J/\psi B_{c}^{\ast +}$ are explored using techniques of QCD sum rule method. These hadronic molecules, composed of only heavy quarks, have asymmetric quark contents $bb\overline{b} \overline{c}$ and $cc\overline{c}\overline{b}$, respectively. The masses $ m=(15864 \pm 85)~\mathrm{MeV} $ and $\widetilde{m}=(9870 \pm 82)~\mathrm{MeV} $ prove that these structures are unstable against dissociations to constituent mesons. Full widths of molecules $\mathcal{M}_{\mathrm{T}}^{ \mathrm{b}}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{c}}$ are calculated by considering their dominant and subleading decay channels. The subleading channels are processes generated by annihilations of $\overline{b}b$ and $ \overline{c}c$ quarks. For the molecule $\mathcal{M}_{\mathrm{T}}^{\mathrm{b} }$ dominant decays are $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}} \to \Upsilon B_{c}^{\ast -}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}} \to \eta_b B_{c}^{-}$, whereas subleading channels are transformations to $\mathcal{M}_{ \mathrm{T}}^{\mathrm{b}}\rightarrow B^{(\ast )-}\overline{D}^{(\ast )0}$ and $\overline{B}_{(s)}^{(\ast )0}D_{(s)}^{(\ast )-}$ mesons. In the case of $ \mathcal{M}_{\mathrm{T}}^{\mathrm{c}}$ we explore decays to $J/\psi B_{c}^{\ast +}$, $\eta_{c}B_{c}^{+}$, $B^{(\ast)+}D^{(\ast )0}$ and $ B_{(s)}^{(\ast )0}D_{(s)}^{(\ast )+}$ mesons. Predictions $\Gamma[\mathcal{M} _{\mathrm{T}}^{\mathrm{b}}]=120^{+17}_{-12}~ \mathrm{MeV} $ and $\Gamma[ \mathcal{M}_{\mathrm{T}}^{\mathrm{c}}]=(71 \pm 9)~ \mathrm{MeV} $ for the widths of these molecules characterize them as relatively broad structures.

The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a framework based on Gaussian Process Regression (GPR) to reconstruct PDFs from lattice QCD matrix elements. Within a Bayesian framework, Gaussian processes serve as flexible priors that encode uncertainties, correlations, and constraints without imposing rigid functional forms. We investigate a wide range of kernel choices, mean functions, and hyperparameter treatments. We quantify information gained from the data using the Kullback Leibler divergence. Synthetic data tests demonstrate the consistency and robustness of the method. Our study establishes GPR as a systematic and non-parametric approach to PDF reconstruction, offering controlled uncertainty estimates and reduced model bias in lattice QCD analyses.