String breaking is at the core of hadronization models of relevance to particle colliders. Yet, studies of string-breaking dynamics rooted in quantum chromodynamics remain fundamentally challenging. Tensor networks enable sign-problem-free studies of static and dynamical properties of lattice gauge theories. In this work, we develop and apply a tensor-network toolkit based on the loop-string-hadron formulation of an SU(2) lattice gauge theory in 1+1 dimensions with dynamical fermions. We apply this toolkit to study static and dynamical aspects of strings and their breaking in this theory. The simple, gauge-invariant, and local structure of the loop-string-hadron states and constraints removes the need to impose non-Abelian constraints in the algorithm, and allows for a systematic computation of observables at increasingly large bosonic cutoffs, and toward the infinite-volume and continuum limits. Our study of static strings yields a determination of the string tension in the continuum and thermodynamic limits. Our study of dynamical string breaking, performed at a fixed lattice spacing and system size, illuminates underlying processes at play during the quench dynamics of a string. The loop, string, and hadron description offers a systematic and intuitive way to diagnose these processes, including string expansion and contraction, endpoint splitting and particle shower, chain scattering events, and inelastic processes resulting from string dissociation and recombination, and particle production. We relate these processes to several features of the dynamics, such as energy transport, entanglement-entropy production, and correlation spreading. This work opens the way to future tensor-network studies of string breaking and particle production in increasingly complex lattice gauge theories.

We present a determination of the charm- and bottom-quark masses using the heavy-quark step-scaling strategy. Renormalization is performed in small volumes where relativistic bottom quarks can be simulated directly. A sequence of finite-volume simulations connects this calculation to large-volume CLS ensembles, where simulations at physical light and strange quark masses provide reliable control over low-energy hadronic physics. In all but the smallest volume, the B-scale is reached by interpolating between relativistic heavy-quark data and the static limit. The resulting quark masses are obtained with good precision, with subdominant systematic uncertainties that differ from, and thus complement, those of standard large-volume determinations.

Lattice simulations and theoretical analyses consistently identify center vortices and monopoles as key nonperturbative configurations in Yang-Mills theory. In the continuum, the effective representation of mixed oriented and nonoriented center vortices showed that these degrees of freedom generate a confining flux tube with $N$-ality. Independently, studies of correlation functions reveal an infrared behavior characterized by massivelike scales. In this Letter, field correlators are computed for the first time in a theoretical framework based on center vortices. Using an Abelian-projected vacuum wave functional peaked on the mixed ensemble, we show the emergence of a massivelike gauge-invariant field strength correlator. For this behavior, the nonoriented component in the center-vortex condensate turns out to be essential, as is also the case for producing the correct properties of confining flux tubes.

Magic and entanglement are two measures that are widely used to characterize quantum resources. We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a given level of entanglement. We quantify magic by the Rényi entropy of order 2, $M_2$, and entanglement by the concurrence $\Delta$. We find that the Pareto frontier of maximal magic $M_2^{(max)}(\Delta)$ is composed of three separate segments, while the boundary of minimal magic $M_2^{(min)}(\Delta)$ is a single continuous line. We derive simple analytical formulas for all these four cases, and explicitly parametrize all distinct quantum states of maximal or minimal magic at a given level of entanglement.

We present an analysis of the light tensor ($J^{PC}=2^{++}$) hybrid meson mass and coupling from QCD Laplace Sum Rules where the next-to-leading order (NLO) perturbative (PT) corrections and the contributions of the non-perturbative (NP) condensates up to dimension-six ($D=6$) are included. NLO leading-logarithms corrections due to the condensates which contribute in the chiral limit are considered. We obtain the mass $M_{2^+}= (2038\pm 190)$ MeV and a relatively small coupling $f_{2^+}=(10.5\pm 2.9)$ MeV normalized as $f_\pi=93$ MeV. Our results suggest that the $f_2(1950)$ or/and the $f'_2(2010)$ may have a sizeable $\bar qqg$ hybrid component. We also compute the tensor hybrid topological charge (value of the two-point function at zero momentum) and find (for the first time) at NLO: $\Pi_{qg}(0)=(2.41\pm 0.43) \times 10^{-4}{\rm GeV}^6$ which could be checked from some lattice QCD or/and low energy theorems (LET).

We demonstrate that the pushforward of the product of Haar measures by the lattice Yang-Mills action concentrates as a Gaussian. It is also sketched how, using this fact, one can recover the strong-coupling expansion.

For a family of two-matrix models \[ \frac{1}{2} \operatorname{Tr}(A^2+B^2) - \frac{g}{4} \operatorname{Tr}(A^4+B^4) - \begin{cases} \frac{h}{2} \operatorname{Tr}( A BA B) \\ \frac{h}{4} \operatorname{Tr}( A BA B+ ABBA ) \\ \frac{h}{2} \operatorname{Tr}( A B BA ) \end{cases} \] with hermitian $A$ and $B$, we provide, in each case, a Monte Carlo estimate of the boundary of the maximal convergence domain in the $(h,g)$-plane. The results are discussed comparing with exact solutions (in agreement with the only analytically solved case) and phase diagrams obtained by means of the functional renormalization group.

We present a lattice-QCD determination of the vector and axial-vector form factors that describe the charm-baryon semileptonic decays $\Xi_c\to \Xi \ell^+ \nu_\ell$. The calculation uses a domain-wall action for the up, down, and strange quarks, and an anisotropic clover action for the charm quark. We use four ensembles of gauge-field configurations generated by the RBC and UKQCD collaborations, with lattice spacings between 0.111 and 0.073 fm and pion masses ranging from 420 to 230 MeV. We present Standard-Model predictions for the decay rates and branching fractions of $\Xi_c^0\to \Xi_c^-\ell^+ \nu_\ell$ and $\Xi_c^+\to\Xi_c^0\ell^+ \nu_\ell$ for $\ell=e,\mu$. In particular, we obtain $\Gamma(\Xi_c^0 \to \Xi^- e^+ \nu_e)/|V_{cs}|^2 = 0.2515(73)\text{ ps}^{-1}$ and $\mathcal{B}(\Xi_c^0 \to \Xi^- e^+ \nu_e) = 3.58(12)\:\%$. These values are higher than those predicted by a previous lattice calculation and substantially higher than the experimentally measured values, but consistent with expectations from approximate $SU(3)$ flavor symmetry.

The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice formulations of strongly interacting theories, such as lattice quantum chromodynamics. In this paper, we prove that the proposal of real-time estimators of scattering observables is universally applicable to all scattering observables of gapped quantum field theories. All finite-volume errors are exponentially suppressed, and the rate of this suppression is controlled by the regulator considered, namely, a displacement of the spectrum of the theory into the complex plane. A partial restoration of Lorentz symmetry by averaging over different boosts gives an additional suppression of finite volume errors. Our results also apply to the simulation of wavepacket scattering, where a similar averaging is performed to construct the wavepackets that regulate the finite volume effects. This result represents a necessary key step towards determining a broad class of scattering observables via quantum computing that are currently inaccessible via classical computing. Such observables are relevant for various applications, including hadron spectroscopy, hadron structure, and precision tests of the Standard Model. We also comment on potential applications of our results to traditional computational schemes.

In this chapter we introduce the $\theta$-dependence and the topological properties of QCD, features of the strongly interacting sector which give rise to the strong CP problem in the more general context of the Standard Model of particle physics. We discuss the analytical approaches that can be used to obtain qualitative, or in some cases quantitative, information on the $\theta$-dependence of QCD and QCD-like models, discussing their range of validity and comparing their predictions with the numerical results obtained by means of lattice simulations.

The complex Langevin method (CLM) is a promising tool to address the sign problem in quantum field theories with complex actions. However, it can converge to incorrect results even when simulations appear stable, highlighting the need for robust diagnostics. Existing checks, such as monitoring drift distributions, are useful but indirect. We propose a complementary test based on the configurational temperature, constructed from the gradient and Hessian of the complex action. Unlike drift-based criteria, this estimator directly probes thermodynamic consistency and provides a physically interpretable cross-check of CLM dynamics. Using one-dimensional PT-symmetric models, we show that it reproduces the input temperature with high precision and sensitively detects algorithmic errors, step-size artifacts, and incomplete thermalization. While demonstrated in simple systems, the method extends naturally to higher-dimensional scalar and gauge theories. Since temperature is tied to the bare coupling in many lattice theories, configurational monitoring can also provide an independent check on coupling-dependent observables. Our results indicate that configurational temperature can enhance CLM reliability across a broad range of applications, including lattice QCD at finite density.

Recent software advances now allow large-scale lattice studies of the Corrigan--Ramond large-$N_C$ limit of Yang-Mills theory coupled with a two-index antisymmetric fermion, providing a path to SUSY Yang-Mills. We are currently generating ensembles for $N_C=4,5,6$ for lattice spacings in the range $0.11 - 0.08$ fm. We report on two aspects of our work: the study of topological properties as well as estimates of discretisation effects. The first aspect is relevant since naively, fractional topological charges might be expected in our simulations. Using a gluonic definition of the topological charge combined with gradient flow, we perform an analysis of the effect of different discretisations of the kernel action, from which we identify and interpret quantitative differences between Wilson and over-improved flows such as DBW2. The second aspect is addressed by considering ratios of different reference flow times. We conclude that our current simulations might be affected by discretisation effects of order 10\%.