In lattice field theory, target distributions are known only up to normalization, (\tilde{\pi}(\phi)\propto e^{-S(\phi)}), while the partition function is intractable. Markov chain Monte Carlo simulations often become inefficient near phase transitions or the continuum limit due to critical slowing down. In this work, we propose a novel sampler based on nonequilibrium thermodynamics, called Stochastic Path Sampler (SPS), which can generate configurations for the unnormalized target distribution without requiring training data. The central idea of SPS is to establish a trajectory-level balance for learnable forward and backward stochastic dynamics between two equilibrium states, namely the prior and target distributions. This is achieved by minimizing the path-space variational free energy, equivalently an entropy-production upper bound, defined by the log-ratio of forward and auxiliary backward trajectory measures, thereby enhancing the reversibility of the forward and backward processes. The learned forward process provides independent proposals, which are subsequently corrected by an extended-space Independence Metropolis--Hastings step. In two-dimensional (\phi^4) theory, we demonstrate that our neural sampler can achieve the same sampling quality as HMC but with a much shorter autocorrelation time in the critical region. This sampler offers a stochastic-quantization-inspired route to data-free proposal construction for lattice field theory by leveraging a variational free-energy principle derived from path-space irreversibility.

We investigate the chemical-potential dependence of hadron spectra in two-color QCD using first-principles lattice simulations. We compute two-point correlation functions for all allowed hadronic operators by newly including the contributions from disconnected diagrams, and extract the corresponding effective masses. In the meson sector, the mass hierarchy in the hadronic phase (normal vacuum) is found to be $m_\pi \lesssim m_{\eta} < m_\sigma \mathrm{(noisy)} < m_\rho \sim m_\omega \ll m_{a_1}$, which is similar to that in three-color QCD. In the superfluid phase, this hierarchy is modified, and with increasing density it changes to $m_\sigma \mathrm{(noisy)} < m_{a_1} < m_\rho < m_\pi \sim m_{\eta} \mathrm{(noisy)} \ll m_{\omega} \mathrm{(noisy)}$. In the diquark sector, the ordering remains as $m_{NG} \lesssim m_{I=0, S} < m_{I=1, AV} < m_{I=0, PS} \lesssim m_{I=0, V}$ in both phases, and the Nambu--Goldstone mode associated with spontaneous breaking of $U(1)_B$ is confirmed to be nearly massless. Furthermore, by comparing correlators for chiral partners, we find indications of chiral symmetry restoration at high density.

Using two distinct approaches, we derive a universal expression for the leading finite-volume effects of the smeared vector-vector spectral density (proportional to the smeared hadronic $R$-ratio) in a periodic cubic spatial volume of side length $L$. First, building on the results of previous work for finite-volume effects on Euclidean two-point functions, we show that the $L$ dependence is exponentially suppressed for a certain class of smearing kernels, and that the leading effects can be expressed universally in terms of the pion form factor. The same representation is then derived starting from the Lellouch-Lüscher-Meyer expression for the spectral decomposition of the correlator. The results may prove useful for controlling the $L \to \infty$ extrapolation of smeared spectral densities, in particular by defining a scaling regime in which the finite-volume effects are dominated by the leading terms in a large $L$ expansion and thus can be reliably estimated. To illustrate this point, we also present numerical estimates based on various kernels and models of particle interactions. Despite focusing on the vector channel, our derivation defines a general framework applicable to other cases as well.

Electric charge fluctuations $\chi_n^Q$ allow comparisons between theory and experiment, but are elusive on the lattice due to severe cutoff effects. We use a 4HEX action to obtain $\chi_2^Q$ and, for the first time ever, $\chi_4^Q$ in the continuum limit. We find disagreement with the hadron resonance gas (HRG) model, which we cannot explain with finite volume effects. We include light meson interactions in the HRG model via the S-matrix, reducing the tension for $\chi_4^Q$, but worsening the agreement for $\chi_2^Q$. We propose measuring the ratio $\chi_4^Q/\chi_2^Q$ at the LHC to investigate this tension.

We apply Lüscher's method to the vector channel of the scattering amplitude of Pseudo-Nambu-Goldstone-Bosons (PNGBs), in the $Sp(4)$ lattice gauge theory coupled to $N_f=2$ flavors of Wilson-Dirac fundamental fermions. We generalize existing algorithms and numerical implementations of the method, to adapt them to this prominent candidate for the completion of proposed extensions of the Standard Model (SM). We present the first ab initio measurements of key properties of the vector resonances in the theory, including the coupling to the PNGBs, that are relevant to direct and indirect new physics searches, both for composite Higgs models (CHMs), as well as for strongly interacting massive particle (SIMP) realizations of dark matter. We also present a global update of the spectroscopy of the mesons in the theory, improving both the statistics and analysis systematics in respect to previous lattice measurements reported in the literature.

We consider a four dimensional $SU(3)$ lattice gauge theory with 12 staggered fermions having identical masses and an unimproved action. Using sets of plaquette distributions for various inverse bare couplings $\beta$, we reconstruct the density of states with the Ferrenberg -Swendsen method and calculate the zeros of the partition in the complex $\beta$ plane with bare quark masses $m_q$ = 0.02, 0.06, 0.08 and 0.1 for hypercubes of linear size $L$= 4, 6, 8, 10, and 12. Our hypothesis is that there is a line of first order transitions in the $(m_q,\beta)$ plane ending at a second order phase transition. We expect this transition to be in the 4D Ising, mean field, universality class. We fit the $L$ dependence of the zeros with the lowest imaginary part using two ($y = bL^{-d}$) and three ($y = a + bL^{-d}$) parameter fits. For $m_q$ = 0.02 the results provide strong support for a first order phase transition ($d=3.98(6)$, and $a$ statistically compatible with 0). The results also indicate, with less statistical significance for $m_q=0.06$, that the three other masses are above the critical value $m_q^c$. In addition, we suggest that the infinite volume gap for the lowest zero $a$, can be represented as $a\simeq A(m_q-m_q^c)^{B}$ with $m_q^c\sim 0.05$ and $B\sim 1$. Given that there are only three data points with significant error bars, it is difficult to rule out the mean field value $B=3/2$. Combining this result with spectroscopic results by Jin and Mawhinney, indicates that the gap with real axis (Lee-Yang edge) scales roughly like $m_\sigma ^2$, where $m_\sigma $ is the mass of the $0^{++}$ scalar which is also the lowest excitation.

In strong magnetic fields, charged quarks occupy the lowest Landau level, leading to an effective dimensional reduction of hadronic dynamics. This dimensional reduction naturally generates a hierarchy of scales, separating fast intra-meson quark dynamics from slow collective meson motion; this motivates a Born-Oppenheimer description of meson-meson systems. Our Born-Oppenheimer analysis shows that the infrared behavior is controlled by the interplay between dimensional reduction and the structure of the meson-meson interaction, leading to three distinct regimes: scattering-dominated, molecular, and compact multiquark states. Charged pseudoscalar mesons such as $\pi_+$ and $K_+$ provide a particularly interesting realization of this framework, as their lattice spectra at large magnetic fields suggest the emergence of loosely bound states near the boundary between scattering and molecular regimes. Our results suggest that strong magnetic fields provide a useful laboratory for exploring the emergence and classification of hadronic bound states.

Contrary to naive expectations, poles used to define hadron resonances rigorously in the physical world may not evolve continuously to become degenerate in the SU(3)$_F$ and chiral limits of QCD. Instead, other shadow poles, usually ignored, may be the ones that degenerate and characterize the resonances in these limits. This feature is general, and we illustrate it first with the simple and familiar light-vector mesons, followed by the much-discussed light-scalar case. Their shadow poles and their degeneracy are found using the QCD low-energy effective theory unitarized to one loop.

We introduce a basis for tree-level meromorphic scattering amplitudes suitable for describing pion scattering in the large-N limit. The basis is constructed as linear combinations of Lovelace-Shapiro-like amplitudes with varying Regge slopes and intercepts. The resulting amplitudes satisfy by construction the fundamental requirements of analyticity, crossing symmetry, and Regge behavior. We analyze their behavior in specific kinematical regimes, including the high-energy fixed-angle limit. We also show that finite linear combinations of our basis elements need not violate unitarity. Nonetheless, because unitarity is not imposed by construction, we enforce it a posteriori by requiring positivity of the partial-wave decomposition. This condition can be formulated as an optimization problem and solved numerically. The solutions to this primal bootstrap problem yield meromorphic amplitudes that satisfy all the aforementioned constraints. We compare several observables with the bounds obtained from the dual positivity conditions and show that our family of amplitudes spans the full allowed parameter space. With appropriate modifications, this method can be extended to construct amplitude families for broader applications.

We investigate the time dependence of anti-flatness in the entanglement spectrum, a measure for non-stabilizerness and lower bound for non-local quantum magic resource, on a subsystem of a linear SU(2) plaquette chain during thermalization. Tracing the time evolution of a large number of initial states, we find that the anti-flatness exhibits a barrier-like maximum during the time period when the entanglement entropy of the subsystem grows rapidly from the initial value to the microcanonical entropy. The location of the peak is strongly correlated with the time when the entanglement exhibits the strongest growth. This behavior is found for generic highly excited initial computational basis states and persists for coupling constants across the ergodic regime, revealing a universal structure of the entanglement spectrum during thermalization. We conclude that quantitative simulations of thermalization for nonabelian gauge theories require quantum computing. We speculate that this property generalizes to other quantum chaotic systems, a conjecture supported by analogous behavior observed in real-time simulations of the mixed-field Ising model.