We study chimera baryons, fermion bound states composed of two (hyper)quarks transforming in the fundamental and one in the antisymmetric representation of a non-Abelian gauge group. While in QCD they coincide with ordinary baryons, in composite Higgs models (CHMs) with top partial compositeness, spin-1/2 chimera baryons serve as partners of the top quark and are responsible for its large mass. We perform non-perturbative lattice calculations of the low-lying spectrum of the chimera baryons, in a specific realization of CHMs based on a Sp(4) gauge theory. In the quenched approximation, we present the numerical results in the continuum and massless limits. Then, for dynamical fermions, we measure the spectrum and matrix elements by employing a newly developed spectral density analysis for several choices of the lattice parameters.

High-precision determinations of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements are essential probes of physics Beyond the Standard Model (BSM). Current precision tests show a deficit in the first row unitarity relation. At the current level of precision, the only relevant CKM matrix elements that contribute to this test are $|V_{ud}|$ and $|V_{us}|$. Without resorting to nuclear inputs, they can be extracted from the combination of the experimental decay width of kaon and pion leptonic decays, along with the theoretical calculation of their decay constants; combined with the decay width of semileptonic kaon decays, with the computation of the corresponding form factor at zero momentum transfer. We review current efforts by the Fermilab Lattice and MILC collaborations towards a correlated analysis of the lattice inputs needed for this test using Highly Improved Staggered Quarks (HISQ) on the $N_f=2+1+1$ MILC configurations along with Staggered Chiral Perturbation Theory (SChPT) as a functional form for the chiral-continuum limit.

Simulating lattice gauge theories on quantum computers presents unique challenges that drive the development of novel theoretical frameworks. The orbifold lattice approach offers a scalable method for simulating SU($N$) gauge theories in arbitrary dimensions. In this work, we present three improvements: (i) two new simplified Hamiltonians, (ii) an encoding of the SU(2) theory with smaller number of qubits, and (iii) a reduction in the requirement for large scalar masses to reach the Kogut-Susskind limit, achieved via the inclusion of an additional term in the Hamiltonian. These advancements significantly reduce circuit depth and qubit requirements for quantum simulations. We benchmarked these improvements using Monte Carlo simulations of SU(2) in (2+1) dimensions. Preliminary results demonstrate the effectiveness of these developments and further validate the use of noncompact variables as a promising framework for scalable quantum simulations of gauge theories.

We present a constituent two-gluon description of the lowest-lying glueball states in pure Yang--Mills theory, calibrated against quenched lattice results. The framework incorporates an instanton-induced dynamical gluon mass, Casimir-scaled adjoint confinement, the short-distance adjoint Coulomb interaction, and instanton-induced central and tensor forces. The scalar $0^{++}$ glueball is found to be exceptionally compact, with a radius of order the instanton size, $\rho \sim \frac 13\,\mathrm{fm}$, consistent with lattice indications. By contrast, the tensor $2^{++}$ state remains spatially extended due to the centrifugal barrier. We also discuss the role of $S$-$D$ mixing. A semiclassical analysis further supports Regge behavior for excited states, in agreement with lattice results.

Lattice gauge theory is an important framework for studying gauge theories that arise in the Standard Model and condensed matter physics. Yet many systems (or regimes of those systems) are difficult to study using conventional techniques, such as action-based Monte Carlo sampling. In this paper, we demonstrate the use of gauged Gaussian projected entangled pair states as an ansatz for a lattice gauge theory involving dynamical physical matter. We study a $\mathbb{Z}_2$ gauge theory on a two dimensional lattice with a single flavor of fermionic matter on each lattice site. For small systems, our results show agreement with results computed by exactly diagonalizing the Hamiltonian, and demonstrate that the approach is computationally feasible for larger system sizes where exact results are unavailable. This is a further step on the road to studying higher dimensions and other gauge groups with manageable computational costs while avoiding the sign problem.

I investigate a $d$-dimensional $U(N)$ Polyakov loop model that includes the exact static determinant with $N_f$ degenerate quark flavor and depends explicitly on the quark mass and chemical potential. In the large $N, N_f$ limit mean field gives the exact solution, and the core of the Polyakov loop model is reduced to a deformed unitary matrix model, which I solve exactly. I compute the free energy, the expectation value of the Polyakov loop, and the quark condensate. The phase diagram of the model and the type of phase transition is investigated and shows it depends on the ratio $\kappa =N_f/N$.

We investigate the spectrum of doubly charmed tetraquark $T_{cc}$ with quantum number $I(J^P) = 0(1^+)$ using MILC's $N_f = 2+1+1$ HISQ gauge ensembles at two lattice spacings. We have included diquark-antidiquark operator together with molecular and scattering operators in our analysis and varied both the heavy and light quark masses. We employ the anisotropic Clover action for heavy quarks, and $O(a)$-improved Wilson--Clover action for the light (up/down) quarks. In order to handle the non-analyticity near the Left Hand Cut we use modified Lüschers method when close to it.

I consider the longstanding issue of the hermiticity of the Dirac equation in curved spacetime. Instead of imposing hermiticity by adding ad hoc terms, I renormalize the field by a scaling function, which is related to the determinant of the metric, and then regularize the renormalized field on a discrete lattice. I found that, for time-independent and diagonal (or conformally flat) coordinates, the Dirac equation returns a pseudo-Hermitian (i.e., PT-symmetric) Hamiltonian when properly regularized on the lattice. Notably, the PT-symmetry is unbroken, ensuring a real energy spectrum and unitary time evolution. This establishes stringent conditions for the existence of complex spectra in 1D non-Hermitian (NH) models. Conversely, time-dependent spacetime coordinates break pseudohermiticity, yielding NH Hamiltonians with nonunitary time evolution. Similarly, space-dependent coordinates lead to the NH skin effect (NHSE), i.e., the accumulation of localized states on the boundaries. Arguably, these NH effects are physical: time dependence leads to local gain and loss processes and nonunitary growth or decay. Conversely, space dependence leads to the NHSE with spatial decay of the fields in a preferential direction. In other words, the curvature gradients induce an imaginary gauge field, corresponding to a drift force acting in space and time, pushing the eigenmodes to the boundaries or forcing their probability density to increase or decrease over time. Hence, temporal curvature gradients produce nonunitary gain or loss, while spatial curvature gradients correspond to the NHSE, allowing for the description of these two phenomena in a unified framework. This also suggests a duality between NH physics and spacetime deformations, framing NH physics in purely geometric terms. This metric-induced nonhermiticity unveils an unexpected connection between the spacetime metric and NH phases of matter.

InflationEasy is a lattice code specifically developed for cosmological inflation. It simulates the nonlinear dynamics of a scalar field on a three-dimensional lattice in an expanding FLRW universe using finite-difference spatial derivatives. Based in part on the well-known LATTICEEASY, it incorporates several features tailored specifically to inflationary applications, including a nonperturbative $\delta N$ method to compute the curvature perturbation at the end of inflation $\zeta$ directly from the lattice. In addition to the scalar sector, the code can also simulate scalar-induced gravitational waves, accounting for contributions generated both during inflation and during the subsequent horizon re-entry of scalar perturbations, and enabling the computation of the resulting gravitational-wave background. \texttt{InflationEasy} enables fully nonlinear studies of regimes with large fluctuations or nonperturbative non-Gaussianities, which lie beyond the reach of standard perturbation theory. It is applicable to a broad range of inflationary models, including those relevant for primordial black hole formation, gravitational-wave backgrounds, and large-scale structure.

The lattice QCD results for the temperature-dependent magnetic susceptibility of the medium below the cross-over temperature are not possible to reconcile with the widely used Hadron Resonance Gas model, also amended with the physical magnetic moments of hadrons or the pion--vector-meson loops. As noticed earlier, one observes a substantially too strong diamagnetism at temperatures in the range above $\approx 120$~MeV compared to the lattice. This hints at a presence of quarks significantly below the QCD cross-over temperature, which are needed as a source of paramagnetism. However, the pions must be retained to describe the diamagnetism data at low temperatures. Therefore, we consider here a quark-meson approach, where the temperature-dependent quark masses are fixed in a model-free way using the baryon-baryon and baryon-strangeness susceptibilities from the lattice at zero magnetic field. The constituent quarks possess anomalous magnetic moments estimated from the octet baryon magnetic moments. The vacuum quark-loop and meson-loop contributions are duly incorporated. We show that in such a framework, one can describe the magnetic susceptibility up to the cross-over point. The qualitative conclusion is that the QCD degrees of freedom must extend far below the cross-over temperature, down to $\approx 120$~MeV.