In this paper we will examine if nonlocal quantum field theory will suffer from the fermion doubling pathology. We find that for a nonlocal Dirac theory, that no additional fermion species are introduced. This is provided that the form factor is nonvanishing at every point. The proof follows from the invertibility of the entire-function operator, which implies that the nonlocal Dirac operator has exactly the same kernel and finite-momentum zero set as the original local Dirac operator. We will distinguish this result from the standard Nielsen-Ninomiya theorem, which applies local lattice Fermions on a compact Brillouin zone. We provide a general criterion for fermion doubling, a test for Genuine and false doubling, and then a test procedure for mathematical and physical fermion doubling. We then will go on to distinguish this result from finite derivative truncations, which can introduce spurious polynomial zeros. We then conclude that fermion doubling is absent in the full continuum nonlocal theory.

We estimate the impact of Polyakov loop (PL) contributions on electroweak phase transitions (PTs). We show that the PL, which is unavoidable in thermal gauge field theory, tends to tame thermal contributions, thereby softening electroweak PTs and affecting bubble dynamics, nucleation, and the related gravitational-wave spectrum. Including this non-perturbative contribution in perturbative approaches results in a thermal effective potential that disfavours first-order PTs over either second-order PTs or smooth cross-overs. This feature is universal for both fermionic and bosonic contributions to the effective potential.

We nonperturbatively compute Rényi entropies for strip-shaped subregions in the three-dimensional O(4) model at finite density on the lattice. By using a dual variable representation and a tailored worm algorithm, we circumvent the sign problem when sampling the grand canonical ensemble. In the limit of large subregions, we also establish a direct, quantitative relationship between the derivative of entanglement entropy with respect to the size of the entangling region and the thermal entropy density for general quantum field theories, providing a new way to study their thermodynamics. We corroborate this argument with our lattice results by demonstrating that, in the appropriate limit, the derivative of entanglement entropy satisfies the same Maxwell relation as the thermal entropy density.

Aoki, Fukaya, and Taniguchi claim that both the spectral density of the Dirac operator at the origin and the topological susceptibility must vanish identically for sufficiently small but nonzero quark mass $m$ in the chirally symmetric phase of quantum chromodynamics with two light quark flavors, under certain technical assumptions on the spectrum and on the dependence of observables on $m$. I argue that a crucial step of their proof is not justified, and the validity of these conclusions should be reassessed. In an additional note I refute the objections raised by S. Aoki and H. Fukaya in their reply to my comment. I show that both the $m^2$-analyticity assumption they invoke against my arguments, and the very claim that these arguments criticize, imply that all local gluonic correlators are independent of the light-quark mass at small mass. This behavior, however, is not observed in quantum chromodynamics. I then show that their claim of having found a mistake in my arguments is baseless.

Ground-state energy and matrix element are reconstructed from correlators in lattice QCD by diagonalizing transfer matrix $\hat{T}$ within the Krylov subspace spanned by $\hat{T}^n|\chi\rangle$, where $|\chi\rangle$ is a state generated by an interpolating field on the lattice. In numerical applications, this strategy is spoiled by statistical noise. To circumvent the problem, we introduce a low-rank approximation based on a singular-value decomposition of a matrix made of the correlators. The associated bias is eliminated by an extrapolation to the limit of vanishing variance of energy eigenvalue. The strategy is tested using a set of mock data as well as real data of $K$ and $D_s$ meson correlators.

As a characteristic property of all quantum systems, entanglement participates in many important quantum phenomena. In this proceeding, we employ it in the study of quantum field theories at finite density. We incorporate evaluations of entanglement entropy using the replica trick into MC simulations of O(N) models at finite density with the worm algorithm and present some initial results for the nonlinear O(4) model in 3 dimensions.

Proton-proton fusion is the fundamental weak reaction initiating stellar energy production, and a first-principles determination of its matrix element remains a long-standing goal of nuclear theory. We present a lattice QCD calculation of the pp fusion matrix element at m_pi~432 MeV. We implement Lellouch-Luscher (LL) finite-volume (FV) corrections within a 2+J->2 framework, accounting for two-nucleon (2N) rescattering, to relate FV matrix elements to infinite-volume counterparts. Excited-state contamination is suppressed using bi-local nucleon-nucleon interpolating operators and a variational analysis with three lowest momenta. This enables determination of 2N energy spectrum and scattering parameters via Luscher's FV formalism. Before including rescattering effects in the LL factor, we obtain /g_A = 0.984(10), where g_A is the axial charge. The deviation from unity indicates a small nonvanishing 2-body current contribution. Our analysis shows that rescattering effects in LL factors substantially modify the 2-body contribution, while large uncertainties in 2N scattering parameters propagate strongly into FV corrections. Thus, precise determination of the 2-body low-energy constant L_{1,A} remains highly challenging with current lattice inputs. Despite the large uncertainty, L_{1,A}=6.0(7.1) fm^3 is compatible, at the level of naturalness, with phenomenological extractions. This work demonstrates feasibility and intrinsic challenges of ab initio lattice QCD calculations of weak 2N reactions, and establishes a foundation for future studies at or near the physical pion mass.

We employ the QCD sum rule method to study the semileptonic weak decay of the single bottom baryon $\Omega_{b}^{*}$ with spin $\frac{3}{2}$ into the single charmed baryon $\Omega_{c}^{*}$ with spin $\frac{3}{2}$, corresponding to a $\frac{3}{2}\rightarrow\frac{3}{2}$ weak transition. A three-point correlation function is calculated in both the physical and theoretical sides to derive the sum rules for the form factors of the transition. The analysis incorporates both the perturbative and non-perturbative contributions up to mass dimension six. After determining the working regions of the auxiliary parameters and performing numerical calculations of the sum rules of the form factors, we extract the $q^2$-dependent fit functions for the form factors. The obtained fit functions are then applied to compute the decay widths of the $\Omega_{b}^{*}\rightarrow\Omega_{c}^{*} \ell \bar{\nu}_{\ell}$ transition in all lepton channels. Our results may serve as useful theoretical benchmarks for future experimental investigations of the semileptonic $\Omega_{b}^{*}\rightarrow\Omega_{c}^{*} \ell \bar{\nu}_{\ell}$ weak decays and the weak dynamics of excited heavy baryons.