Yang-Mills theories at $\theta$ and $\theta+2\pi$ are unitarily equivalent, but their $2\pi$ periodicity has a nontrivial realization. Recent developments in generalized global symmetries show that confinement vacua at $\theta=0$ and $2\pi$ should belong to different symmetry-protected topological (SPT) states with the $1$-form center symmetry. For its examination, we measure the Wilson-'t Hooft loop operators at $\theta=2\pi$ for the $SU(2)$ Wilson lattice gauge action and discuss their long-distance behaviors. This requires us to identify the gauge topological charge in the presence of defects, and we employ the $1$-form covariant DBW2 gradient flow to smear lattice gauge fields. We then obtain numerical evidence consistent with dyon condensation at $\theta=2\pi$, rather than monopole condensation, as theoretically predicted.

We study decomposition of the nonabelian gauge field into the Abelian component created by Abelian monopoles and the modified nonabelian components with monopoles removed after fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics. We compute the static potential V (r) for the original gauge field and for its components V_mon and V_mod at two values of the lattice spacing. We confirm that with optimal gauge fixing the sum V_mon + V_mod deviates substantially from V(r). We show that this decomposition of the static potential is satisfied with good precision at all distances when we use another set of Gribov copies.

A key property of a global symmetry's anomaly is its order: the smallest integer $n$ for which the diagonal symmetry of the $n$-copy system is anomaly-free. While many familiar lattice anomalies have finite order, perturbative anomalies in the continuum$-$those captured by Feynman diagrams$-$have infinite order. In this paper, we show that the Onsager symmetry, a lattice realization of the chiral symmetry of a 1+1d massless Dirac fermion, has an order-two anomaly. However, imposing lattice CPT symmetry enhances this anomaly from order two to infinite order, yielding a lattice chiral symmetry structure that more faithfully matches the continuum chiral anomaly. We also discuss the corresponding 2+1d symmetry-protected topological phases for these infinite-order lattice anomalies.

We study the analytic structure of the QCD phase diagram by treating temperature as a complex variable. The nearest Yang-Lee edge singularities in the complex $T$ plane bound the domain of analyticity of temperature-dependent thermodynamic observables and complement the more commonly studied singularities in the complex chemical-potential plane. Our analysis combines three complementary perspectives: universal critical scaling, a first-principles extraction from lattice-QCD data, and explicit illustrations in effective models. We illustrate the resulting structure in a random-matrix model and in a quark-meson model, where the singularity trajectories can be followed explicitly. At small real chemical potential, the leading complex-temperature singularity admits an analytic expansion in $\mu^2$, while near a critical point it crosses over to the universal Puiseux form dictated by Ising critical scaling. We show that the complex-$T$ and complex-$\mu$ trajectories are controlled by the same scaling variables and mapping coefficients, so their comparison provides a stringent consistency test of critical-point searches and constrains the extent of the critical scaling regime. Finally, we analyze lattice-QCD data at $\mu=0$ using an iterated conformal-Pade approach and extract the continuum location of the nearest complex-temperature singularity. The result is consistent with the expectation that, at physical quark masses, the real part of the leading singularity lies between the chiral-limit transition temperature and the physical-mass chiral-susceptibility peak temperature, while its imaginary part remains nonzero.

The calculation of inclusive processes that involve the production of many particles is a challenge for lattice QCD, a Euclidean-space method that is far removed from real-time, multiparticle production. A new approach to this problem based on Nevanlinna-Pick interpolation has been proposed by Bergamaschi et al. Here we extend their method by exploring the propagation of the statistical and systematic errors that accompany a lattice QCD calculation through this interpolation process. A simplified example of a multiparticle spectral function is studied with a focus on the possible applications of these methods to the calculation of inclusive heavy-particle decays.

We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$ in the confining phase of the theory in the infinite $N$ limit. Exploiting the symmetries of these models and applying nonlinear relaxation, we impose constraints that include traces of words of length up to 14. Our results yield rigorous bounds on the large-$N$ ground-state dynamics, along with estimates of selected low-order observables to eight significant digits.

We construct two quantum error correction codes for pure SU(2) lattice gauge theory in the electric basis truncated at the electric flux $j_{\rm max}=1/2$, which are applicable on quasi-1D plaquette chains, 2D honeycomb and 3D triamond and hyperhoneycomb lattices. The first code converts Gauss's law at each vertex into a stabilizer while the second only uses half of the vertices and is locally the carbon code. Both codes are able to correct single-qubit errors. The electric and magnetic terms in the SU(2) Hamiltonian are expressed in terms of logical gates in both codes. The logical-gate Hamiltonian in the first code exactly matches the spin Hamiltonian for gauge singlet states found in previous work.