We study conserved charges of the staggered fermion Hamiltonian in 3+1 dimensions. By decomposing staggered fermions into Majorana components and exploiting lattice translation symmetries, we construct a set of conserved non-singlet charges. We analyze their algebra andshow that, although the charges exhibit nontrivial non-commutativity on the lattice, they generate axial SU(2)_L \tines SU(2)_R transformations for low-energy degrees of freedom in the continuum limit. Possible implications for anomalies are discussed.

We investigate the Hamiltonian formulation of 1+1-dimensional staggered fermions and reconstruct the vector and axial charge operators, originally identified by Arkya Chatterjee et al., within the Wilson fermion formalism. These operators commute with the Hamiltonian and reduce, in the continuum limit, to the generators of the vector and axial $\mathrm{U}(1)$ symmetries. A notable feature of the axial charge operator is that it acts locally on operators and possesses quantized eigenvalues. Its eigenstates can therefore be interpreted as fermion states with well-defined integer chirality, analogous to those in the continuum theory. This structure enables the formulation of a gauge theory in which the axial $\mathrm{U}(1)_A$ symmetry is promoted to a gauge symmetry. We construct a Hamiltonian in terms of the eigenstates of the axial charge operator, thereby preserving exact axial symmetry on the lattice while recovering vector symmetry in the continuum limit. As applications, we study the implementation of the Symmetric Mass Generation (SMG) mechanism in the 3-4-5-0 models. Our framework admits symmetry-preserving interaction terms with quantized chiral charges, although further numerical investigation is required to confirm the realization of the SMG mechanism in interacting systems.

We present our ongoing work on two-dimensional maximally supersymmetric Yang-Mills (2D MSYM) theory using lattice techniques. The continuum theory is obtained from the dimensional reduction of four-dimensional ${\mathcal N} = 4$ supersymmetric Yang-Mills theory. We construct both the continuum and lattice versions of the 2D MSYM theory. The lattice action preserves a subset of supersymmetries. We extend existing lattice software with new routines to accommodate the additional terms in the lower-dimensional theory. This lattice construction enables us to perform Rational Hybrid Monte Carlo simulations of 2D MSYM and facilitates the exploration of its continuum limit. Our work contributes to the numerical study of maximally supersymmetric gauge theories and supports the ongoing efforts to test gauge-gravity duality and investigate related non-perturbative phenomena.

We present the nucleon strange electromagnetic form factors using four lattice QCD ensembles with $N_f=2+1+1$ twisted mass clover-improved fermions and quark masses tuned to approximately their physical values. The four ensembles have similar physical volume and lattice spacings of $a=0.080$ fm, $0.068$ fm, $0.057$ fm and $0.049$ fm allowing us to take the continuum limit directly at the physical pion mass point. We compute nucleon three-point correlation functions with high statistics, where the disconnected fermion loops are evaluated stochastically with spin-color dilution and hierarchical probing. We find non-zero values for both electric and magnetic form factors. We extract the strange electric and magnetic radii, as well as the strange magnetic moment in the continuum limit by studying the momentum dependence of the form factors. We also compute the charm electromagnetic form factors within the same setup, which we find to be consistent with zero within the statistical precision of our data.

We present the strange electromagnetic form factors of the nucleon using lattice QCD simulations with degenerate light, a strange, and a charm quark in the sea with masses tuned to their physical values. For the first time, the strange electromagnetic form factors are computed at the continuum limit using only ensembles simulated with physical quark masses, eliminating the need for chiral extrapolations and their associated systematic uncertainty. We obtain the momentum transfer dependence of the form factors using the $z$-expansion and provide the strange electric and magnetic radii, as well as the strange magnetic moment. When combining our statistical errors and systematic uncertainties stemming from the momentum transfer dependence fit, our errors are an order of magnitude smaller than those associated with experimental determinations of the strange electromagnetic form factor.

We report on the status of an update of our collaboration's previous computation of light and strange quark masses in QCD with $N_{f}=2+1$ dynamical flavours. Bare quark masses are extracted from CLS ensembles, using $O(a)$-improved Wilson fermions, and the mass renormalization is performed non-perturbatively in the Schrödinger functional scheme over a wide range of scales to make safe contact with perturbation theory. Results for five lattice spacings, down to $a\sim 0.038 \textrm{ fm}$, and pion masses reaching the physical value are included in the analysis. This allows for the exploration of different models for cutoff and chiral effects, and a controlled extrapolation to the physical point.

Using a symmetry preserving treatment of a vector*vector contact interaction (SCI), results are delivered for the four kaon transverse momentum dependent parton distribution functions (TMDs), viz. helicity-independent (HI) and Boer-Mulders (BM) TMDs for the kaon's $u$, $s$ valence degrees of freedom. In completing this analysis, we are able to deliver insights into, amongst other things, the role played by emergent hadron mass (EHM) phenomena in producing these TMDs; the EHM modulating effect of the Higgs-boson coupling that produces the strange quark current mass; the impact of gauge link models on whether predictions satisfy the positivity constraint that bounds the BM function relative to the HI TMD; and the size of the BM shift and effects thereupon of off-diagonal terms in the associated scale-evolution kernel.

We investigate the universal features of chiral symmetry breaking in large-$N$ QCD by comparing non-perturbative determinations of the low-lying Dirac spectrum with chiral Random Matrix Theory (RMT) predictions. Our numerical Monte Carlo calculations are based on a chiral lattice discretization of the Dirac operator, and exploit twisted volume reduction to reach $N$ as large as 841. Matching lattice data with RMT analytic results, we are able to extract the large-$N$ chiral condensate, which is compared with a recent determination obtained with non-chiral Wilson quarks from twisted volume-reduced models.

We set the scale of SU($N$) Yang--Mills theories for $N=3,5,8$ and in the large-$N$ limit via gradient flow, as a first step towards the computation of the large-$N$ $\Lambda$-parameter using step scaling. We adopt twisted boundary conditions to achieve large-$N$ volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as $\sim 0.025$ fm for all the explored values of $N$, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-$N$ twisted volume reduction.