Lattice gauge theories (LGTs) provide a powerful framework for studying non-perturbative phenomena in gauge theories. However, conventional approaches such as Monte Carlo (MC) simulations in imaginary time are limited, as they do not allow real time evolution and suffer from a sign problem in many important cases. Using Gauged Gaussian fermionic projected entangled pair states (GGFPEPS) as a variational ground state ansatz offers an alternative for studying LGTs through a sign-problem-free variational MC. As this method is extended to larger and more complex systems, understanding its numerical behavior becomes essential. While conventional action based MC has been extensively studied, the performance and characteristics of non-action-based MC within the GGFPEPS framework are far less explored. In this work, we investigate these algorithmic aspects, identifying an optimal update size for GGFPEPS-based MC simulations for $\mathbb{Z}_2$ in $2+1$ dimensions. We show that gauge fixing generally slows convergence, and demonstrate that not exploiting the translation-invariance can, in some cases, improve the computational time scaling of error convergence. We expect that these improvements will allow advancing the simulation to larger and more complex systems.

We discuss recent developments regarding the use of kernels in complex Langevin simulations. In particular, we outline how a kernel can be used to solve the problem of wrong convergence in a simple toy model. Since conventional correctness criteria for complex Langevin results are only necessary but not sufficient, the correct convergence of complex Langevin simulations is not always straightforward to assess. Hence, we furthermore discuss a condition for correctness that we have recently derived, which is both necessary and sufficient. Finally, we outline a machine-learning approach for finding suitable kernels in lattice gauge theories and present preliminary results of its application to the heavy-dense limit of QCD.

The rare decays $\eta^{(\prime)}\to\ell^+\ell^-$, $\ell\in\{e,\mu\}$, are highly suppressed in the Standard Model, both by their chirality structure and the required loop attaching the lepton line to the $\eta^{(\prime)}\to\gamma^*\gamma^*$ matrix element. The latter is described by a single scalar function, the transition form factor, which has recently been studied in great detail for $\eta^{(\prime)}$ in the context of the pseudoscalar-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. Based on these results, we evaluate the corresponding prediction for the $\eta^{(\prime)}$ dilepton decays, supplemented by an improved evaluation of the asymptotic contributions including pseudoscalar mass effects. In particular, the dispersive representation for the $\eta^{(\prime)}$ transition form factors allows us, for the first time, to perform a robust evaluation of the imaginary parts due to subleading channels besides the dominant two-photon cut. Our final results are $\text{Br}[\eta\to e^+e^-]=5.37(4)(2)[4]\times 10^{-9}$, $\text{Br}[\eta\to \mu^+\mu^-]=4.54(4)(2)[4]\times 10^{-6}$, $\text{Br}[\eta'\to e^+e^-]=1.80(2)(3)[3]\times 10^{-10}$, and $\text{Br}[\eta'\to \mu^+\mu^-]=1.22(2)(2)[3]\times 10^{-7}$, where the errors refer to the uncertainty in the normalized branching fraction, the one propagated from $\text{Br}[\eta^{(\prime)}\to\gamma\gamma]$, and the total uncertainty, respectively. The branching fraction for $\eta\to\mu^+\mu^-$ exhibits a mild $1.6\sigma$ tension with experiment, and we explore the bounds that can be derived on physics beyond the Standard Model.

Poincaré-covariant Bethe-Salpeter wave functions are used to calculate light-front wave functions (LFWFs) of the pion, $\pi$, and an analogue state, $\pi_{s\bar s}$. The current masses of the degenerate valence constituents in the $\pi_{s\bar s}$ are around $25$-times larger than those of the pion's valence constituents. Both valence spin-antialigned ($\mathcal L=0$) and valence spin-aligned ($\mathcal L=1$) components are obtained and combined to produce the complete LFWF for each system. Comparing predictions delivered by two distinct Bethe-Salpeter kernels, the impact of nonperturbative dynamical effects contained in the more sophisticated (bRL) kernel are seen to be significant; and contrasts between $\pi$, $\pi_{s \bar s}$ results reveal the interplay between emergent hadron mass and mass effects owing to Higgs-boson couplings. Amongst the results, one finds that for $\pi$, $\pi_{s\bar s}$, the LFWFs can be approximated by a separable form, with that representation being pointwise reliable in the bRL cases. Moreover, the $\mathcal L=1$ component is important; so a LFWF obtained after omission of this piece is typically a poor representation of the system. These features are naturally expressed in $\pi$, $\pi_{s\bar s}$ transverse momentum dependent parton distribution functions (TMDs). In this connection, it is found that a Gaussian \textit{Ansatz} can only provide a rough guide to TMD pointwise behaviour: magnitude deviations between \textit{Ansatz} and prediction exceed a factor of two on $k_\perp^2 \gtrsim 0.55\,$GeV$^2$. One should therefore be cautious in interpreting conclusions drawn from phenomenological analyses based upon Gaussian \textit{Ansätze}.

We provide a detailed analysis of the gravitational wave spectrum of $SU(N)$ pure Yang-Mills theory. The confinement phase transition is described with an effective Polyakov loop model, using the latest lattice data as an input. In particular, recent lattice studies clarified the large-$N$ scaling of the surface tension, which we incorporate through a modification of the kinetic term. We demonstrate that the thin-wall approximation agrees with the Polyakov loop model at small $N$ while it breaks down at large $N$. Furthermore, we include reliable estimates of the bubble wall velocity using a recently developed framework based on a large enthalpy jump at the phase transition. Altogether, this allows us to derive the gravitational wave signals for all $SU(N)$ confinement phase transitions and clarifies the behaviour at large $N$. The strongest signal arises for $N=20$, but overall the predicted signals remain rather weak. Our work paves the way for future studies of other gauge groups and systems with fermions.

We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the left-hand cut issue arising from long-range potential, which are challenging in the framework of standard Lüscher formula. Furthermore, the method provides a foundation for further extension to three-particle systems. We first benchmark our method by examining several toy models, demonstrating its consistency with standard Lüscher formula in the absence of long-range potential. In the presence of long-range potential, we investigate and resolve the effects and issues of left-hand cut. As a realistic application, we calculate the finite volume spectra of isoscalar $D\bar{D}^*$ system, where the well-known exotic state $\chi_{c1}(3872)$ is observed. The results are qualitatively consistent with the lattice QCD calculation, highlighting the reliability and potential application of our framework to the study of other exotic states in hadron physics.

We present a major update on the spectrum of closed flux tubes in $D=3+1$ $SU(N)$ gauge theories. We measure the excitation spectrum of confining strings wound around a spatial dimension of a size $R$. We do so for the $SU(N)$ Yang-Mills theory with $N=3,5,6$ and for two different values of the lattice spacing. We employ the generalized eigenvalue problem in combination with an extended basis of operators; this enables us to project onto all possible irreducible representations characterised by spin $|J_{\rm modulo \ 4}|$, transverse parity $P_{\perp}$, longitudinal parity $P_{\parallel}$ as well as by longitudinal momentum $p_{\parallel}=\frac{2 \pi q}{R}$, and extract accurate results for approximately $35$ lightest states. Applying the Thermodynamic Bethe Ansatz (TBA) technique for calculating the finite volume spectrum, we confirm that the observed states are well described by the low energy effective theory of a long string consisting of two translational Goldstone bosons (``phonons"), along with a massive pseudoscalar (``the worldsheet axion") coupled to phonons through a $\theta$-term. Moreover, we find that the leading axion-axion and axion-phonon interactions are well approximated by the $T\bar{T}$ deformation of a free axion.

Quantum computers are expected to be vital for exploring complex dynamics in many-body quantum systems. Thus, validating established results on current quantum computers is essential for evaluating their future utility. Hence, we investigate the entanglement entropy of the Sachdev-Ye-Kitaev (SYK) model, a paradigmatic model of quantum chaos, many-body physics, and holographic duality, in current IBM's superconducting quantum computers. We implement optimized swap-based many-body interference protocol and randomized measurement protocol tailored for IBM quantum computers' limited qubit connectivity. Additionally, we employ quantum multi-programming that parallelizes circuit execution to improve the results obtained by the randomized measurement protocol. Finally, by incorporating the quantum error mitigation techniques into our implementation of the entropy measurement protocols on IBM quantum hardware, we show that the current noisy quantum computer can yield results aligned with theoretical expectations, therefore affirming its capability to explore chaotic quantum dynamics in complex quantum systems.