Papers

We present a model-independent calculation of $\pi N$ forward dispersion relations and their analytic continuation to the complex plane, using a revised set of $\pi^\pm p$ total cross-section data up to 3 GeV, and Regge asymptotics above. Up to that energy, we find four stable poles for each isospin combination. The lightest pole in the $I=3/2$ channel corresponds to the $\Delta(1232)$ resonance, while the lightest in the $I=1/2$ channel corresponds to the Roper resonance, even though the latter is imperceptible in the data. We extract their pole parameters and the parameter difference between the $\Delta^0$ and $\Delta^{++}$, without relying on a partial-wave analysis. The remaining poles cannot be identified with a single resonance each. They are not artifacts but the combined effect of multiple resonances unresolved by total cross-section data alone. Finally, we write sum rules relating the residues of these constituent resonances to the residues of the poles extracted from the dispersive representation.

Though quantum computing naturally offers an advantage for simulations of real-time quantum systems, implementing Imaginary-Time Evolution (ITE) is comparatively more difficult. Nevertheless, quantum implementations of ITE are useful both in cases where classical implementations have associated sign problems, and also as an exact method of preparing eigenstates on quantum computers. In this work we present an algorithm to obtain ITE of a generic quantum Hamiltonian by performing analytic continuation of measured real-time correlation functions. We present simulations and demonstrations on IBM quantum hardware of 1D Fokker-Planck equations for classical diffusion process and imaginary-time evolution of integrated correlation functions in 1D quantum mechanical scattering as examples to demonstrate the effectiveness of the method.

We examine the formulation of Kähler fermions on spacetimes with Lorentz signature. In practice we focus on Minkowski spacetime since most of the difficulties that are encountered are visible even when the spacetime is flat. We show that the theory, when interpreted as a Lorentz invariant theory of forms or antisymmetric tensor fields, is non-unitary. We show that unitarity can be restored provided one adopts a modified inner product on the Hilbert space. This modified inner product requires the insertion of an operator J that anti-commutes with certain modes of the Kähler field in such a way as to guarantee all states have positive norm. We give an explicit (and local) form for J and show that while it commutes with the Hamiltonian, it is incompatible with the Lorentz transformation properties of the tensor fields. In flat space, the unitarized formulation is equivalent to 4 Dirac fermions.

We present the first application of the unbiased exponential resummation method to the determination of the QCD pseudocritical temperature $T_{\rm pc}$ at vanishing baryon chemical potential $\mu_B$. By reconstructing the finite-density baryon number susceptibility $\chi_2^B$, we define two thermal-derivative observables whose peak positions yield $T_{\rm pc}^T=160.2(4)(3)$ MeV and $T_{\rm pc}^C=158.1(5)(3)$ MeV. We also show that the pseudocritical temperature, $T_{\rm pc}^\chi$ obtained from the peak of the fourth-order baryon number susceptibility $\chi_4^B$ is consistent with these determinations and with previous lattice-QCD results based on Taylor expansions \cite{Bollweg:2022Pade}. Further, we demonstrate that scaling relations \cite{Bollweg:2022fqq} between $\chi_4^B$ and the thermal derivatives of $\chi_2^B$ yield mutually consistent estimates of the leading second order curvature coefficient $\kappa_2^B$ at the corresponding pseudocritical temperatures. A direct analysis of the $\mu_B$ dependence of the pseudocritical temperatures provides an independent but substantially less constrained determination of the curvature, which remains statistically consistent with the scaling-based estimates. These results demonstrate the consistency of unbiased exponential resummation with the expected scaling behavior and establish it as a complementary approach for probing the QCD crossover at small finite baryon density.

Many rigorous results in the modern era of statistical mechanics have been obtained through geometrical representations. A much studied tool in this setting is the random cluster representation of lattice spin models. Another area of statistical mechanics that is of great interest but lacking rigorous results is the theory of the renormalization group. This paper investigates the idea to find a common ground between these two concepts in order to obtain rigorous results on the renormalization group flow. A need for negative cluster-weights weakens the success of this approach. Nevertheless, we managed to establish a relation between the scaling limit of the renormalization group flow of the nearest-neighbour Ising model away from criticality with a simple one-dimensional dynamical system that follows the cluster connectivity of the renormalization group transformation. This allows for a rigorous proof of the convergence of this flow to the zero- and infinite-temperature fixed point respectively for a large family of renormalization group transformations. Explicit results will be established on $\mathbb{Z}^2$ followed by a discussion of the available generalizations to higher dimensions.

We conduct numerical simulations to map out the phase diagram and critical behavior of a lattice Higgs model composed of two massless staggered fermion fields forming a doublet under a global $SU(2)$ and coupled to a scalar field in the adjoint representation of the group. The scalar action consists of a potential comprising quadratic and quartic terms and a scalar kinetic term. At fixed quartic coupling we explore a two-dimensional parameter space finding a massless symmetric phase at weak coupling and a massive symmetric phase (SMG phase) at strong coupling. An intermediate anti-ferromagnetic phase separates these two regimes. These results are consistent with leading order weak and strong coupling expansions. We find that the critical lines bounding the intermediate phase merge at a unique point where all fermion bilinear condensates vanish but fermion susceptibilities diverge as non-trivial powers of the lattice size. We conjecture that this merged point corresponds to a multicritical point and may describe a phase consisting of a condensate of certain topological defects.

We investigate signatures of chirality at Chern insulator transitions in the presence of a boundary. The transition between a trivial insulator and a Chern insulator with Chern number $C=1$ is described by a massless Dirac fermion whose parity anomaly gives a critical Hall conductivity $\sigma_{xy}=\frac{1}{2}\frac{e^2}{h}$. Using a Dirac mass domain wall construction, we show that the chiral edge mode delocalizes into the bulk at criticality, but the boundary fermion correlation function retains a chiral structure and acquires the scaling dimension of the bulk fermion. We compute current correlation functions and demonstrate that the anomaly of the bulk Hall response is matched by delocalized chiral modes near the boundary. Using only the residual conformal symmetry of a (2+1)d conformal field theory (CFT) in a half-space, we identify parity-odd terms in current and energy-momentum tensor correlation functions that encode these modes and determine their electromagnetic and gravitational anomaly coefficients. Our analysis therefore applies to general time-reversal breaking (2+1)d CFTs, beyond the free Dirac transition. In particular, the analysis of the gravitational anomaly is also applicable to the free Majorana CFT governing the transition between a trivial superconductor and a topological superconductor. We also extend our results to more general Chern number changing transitions and to the transition between a (3+1)d topological insulator and a trivial insulator.

We propose a Z-transform framework for the analysis and synthesis of finite range lattice momentum operators in quantum field theory. In this formulation, translation-invariant lattice operators are represented as functions of the complex variable $z$ in the unit circle, allowing their spectral properties to be analyzed using tools from digital signal processing and rational approximation theory. Within this framework, the fermion doubling problem is reinterpreted as the appearance of unwanted zeros of the discrete momentum operator on the unit circle — an aliasing phenomenon in the sense of the Nyquist sampling theorem — and the conditions for ghost suppression are expressed as precise constraints on the zero structure of the operator's transfer function. It is proven that no rational function can satisfy all required conditions simultaneously, motivating the finite impulse response approach developed here. This reframing naturally suggests a class of finite-range momentum operators, constructed by solving a least-squares approximation problem in the frequency domain. The resulting finite impulse response (FIR) operator approximates the continuum derivative across the full Brillouin zone, with ghost suppression achieved through the accuracy of the spectral approximation rather than through the addition of a symmetry-breaking Wilson term or the infinite-range nonlocal SLAC derivative. Numerical investigation confirms that near $\theta = \pi$ only plane waves propagate coherently, and these exhibit group velocities far exceeding the speed of light, further distinguishing them from physical low-energy excitations. No ghost wave packet solutions exist near $\theta = \pi$.

Gauge theories like lattice QCD present a complex problem for quantum simulation. In a basis where the electric part of the Hamiltonian is simple, the magnetic part, generally expressed as a sum over the plaquette operators of the lattice, is quite complicated, producing correlated transitions between several link and site degrees of freedom. We provide an efficient block encoding of the plaquette operator in the irrep basis, a refinement of the electric basis where the internal gauge-variant degrees of freedom are integrated out. The construction removes the plaquette matrix element scaling wall which has been a significant barrier for other approaches in this basis. The algorithm leverages a convenient factorization property of the matrix elements, cheap classical precomputation, and quantum oracles built from lookup tables and programmed rotations.

The simple Ising model provides a rich environment to build and study lattice field theories. As part of an ongoing project to construct a conformal field theory (CFT) on an arbitrarily curved manifold, in this work we develop methods to measure the critical temperature $\beta_c$ of the affine-transformed Ising model on the face-centered cubic (FCC) lattice. The main challenge in this endeavor is finding a computationally efficient and accurate method of interpolating and extrapolating Monte Carlo observables with respect to coupling coefficients and temperature. Herein, we compare two such methods. A traditional statistical approach uses the multiple histogram (MH) method, while a newer machine learning approach uses a masked autoregressive flow (MAF) to estimate the underlying probability density function of a set of observables. While the MH method is specifically designed to interpolate and extrapolate Monte Carlo observables, we find that MAF is a viable alternative for measuring $\beta_c$ with a computational cost that scales more favorably. Furthermore, we comment on additional advantages of MAF relevant to our work, such as extrapolating in system volume.

We study interacting scalar quantum field theories in anti-de Sitter (AdS) space using a tensor-network approach based on matrix product states. We develop methods for extracting low-lying boundary spectra from global-AdS energy levels, probing bulk criticality through finite-size scaling in the AdS radius, and identifying conformal boundary conditions. Applying these methods to scalar $\phi^4$ theory in $\mathrm{AdS}_2$, we compute the lowest non-trivial $\mathbb{Z}_2$-odd and even boundary scaling dimensions non-perturbatively. We then locate the bulk $\mathbb{Z}_2$ symmetry-breaking transition and extract critical exponents and central charge consistent with the 2D Ising universality class. At the critical point, we determine the low-lying boundary spectrum and use it to identify the $\mathbb{Z}_2$-preserving free/ordinary Ising conformal boundary condition, thereby characterising both the bulk and boundary universality classes.

That the gluons of quantum chromodynamics self-interact with a strong coupling suggests the possibility of hadrons in which the gluonic field plays an essential role: Glueballs in which gluons stick together to produce a hadron in which no quarks are required, and hybrids in which an excited gluonic field couples to quarks. This chapter presents our contemporary theoretical understanding of such states, and the challenges associated with definitively identifying their presence within the experimental spectrum of hadrons.

We study quantum simulation of SU(3) non-Abelian gauge theory dynamically coupled with fundamental fermions in $3+1$ dimensions by employing the lattice Hamiltonian in axial gauge that avoids Gauss's law constraints. The temporal component of the gauge field is analytically solved in terms of independent field degrees of freedom and a lattice regulated Green's function. The axial gauge condition is trivially maintained in time evolution, even under Trotterization. The gauge field degrees of freedom are expressed in the local field basis and can be efficiently transformed into the canonical conjugate momentum basis by local quantum Fourier transforms. We prove the number of qubits needed for describing all states up to an energy $E$ with an accuracy $\epsilon$ on a lattice of volume $V$ at bare coupling $g$ is bounded as $16n_A V + 12n_f V$, where $n_A \approx \log_2 (\frac{64 E' V^{4/3}}{\pi^2\epsilon} + \frac{32\sqrt{2}g n_f E'^{1/2} V^{7/6}}{\sqrt{3}\pi^3\epsilon^{1/2}} ) $ is the number of qubits needed for each independent gauge field per site with a shifted energy $E'$, and $n_f$ denotes the number of fermion flavors. We then analyze a quantum algorithm for time evolution that is based on Trotterization, quantum Fourier transform, and Jordan-Wigner transformation, for which quantum circuits can be explicitly constructed under arbitrary gauge field truncation and digitization. We find the numbers of CNOT and single-qubit rotation gates both scale as $O(n_A^4 V^{4/3}) + O(V^{5/3})$ per Trotter step for fixed $n_f\leq 6$. We conclude that quantum resources needed for simulating real-time dynamics of lattice QCD scale polynomially with volume, energy, time, accuracy, and bare Hamiltonian parameters.

We investigate the configurational temperature estimator as a diagnostic tool for Monte Carlo and Langevin simulations of the three-dimensional XY model with an imaginary chemical potential. This estimator depends only on the field configurations. It provides a stringent internal consistency check for numerical sampling algorithms. We perform simulations using both real Langevin dynamics and the Metropolis Monte Carlo algorithm on an $8^3$ lattice across a range of coupling values, $\beta = 0.2 - 0.7$. Our results for the action density are in excellent agreement with strong-coupling expansion predictions at small $\beta$, providing an important validation of both simulation approaches. The measured value of the configurational temperature estimator shows good agreement with its expected value of unity in the symmetric phase. However, systematic deviations appear in the ordered phase. We attribute these deviations primarily to finite-size effects and discretization artifacts associated with the relatively small lattice volume. Our results demonstrate that the configurational temperature estimator provides a valuable diagnostic for assessing thermalization and algorithmic correctness in lattice field theory simulations. Such diagnostics are particularly important in preparation for studies at real chemical potential, where sign problems arise and conventional validation methods become less reliable.

Higher-form symmetries generalize conventional global symmetries and act on lower-dimensional submanifolds of a quantum system. While Abelian topological phases can be organized by 1-form symmetries that form a group, non-Abelian topological phases based on finite groups require 1-form symmetry operators governed by non-invertible fusion algebras. In this work, we make this statement precise in quantum double lattice models $\mathcal D(G)$ for finite non-Abelian groups $G$. We construct the electric, magnetic, and dyonic 1-form operators directly at the lattice fixed point and show that together they form a complete nonlocal diagnostic algebra for the topological Hilbert space. Using these operators, we explicitly determine the cylinder and torus ground-state subspaces for arbitrary finite $G$. Furthermore, we calculate the microscopic fusion and gluing of the 1-form symmetries and show that their topological deformation properties emerge after projection to the defect-free topological subspace. Our results establish ground states of non-Abelian quantum double models as a concrete microscopic realization of spontaneous non-invertible 1-form symmetry breaking and provide an operator language that may be useful for characterizing such states in quantum processors.

We construct the natural generalization of stochastic quantization (in the Markovian sense) by considering jump-diffusion processes. This class of stochastic processes exhibits non-continuous paths, so-called Lévy flights. In the presence of jumps, action landscapes with barriers can be efficiently explored, improving and even restoring ergodicity where traditional diffusion approaches become inefficient. We explore different strategies for constructing efficient jump updates, which we deploy to address the benchmark problem of topological freezing in 2d U(1) gauge theory.

We identify the dynamical origin of amplified isospin breaking in near-threshold states. Using a pole-residue-based measure defined directly from the pole couplings, rather than from decay observables that are also affected by different final-state kinematics, we show that threshold proximity of the pole alone is insufficient: large isospin breaking requires a sizable interaction in the companion isospin channel. Applied to the $X(3872)$, the observed large isospin breaking points to a nearby partner pole, $W_{c1}$, as predicted in previous studies. In addition, we find that the $W_{c1}$ pole, which predominantly affects the line shapes near the charged threshold in the physical case, does not evolve into the pure $I=1$ eigenstate in the isospin limit; instead, that eigenstate is continuously connected to a more distant shadow pole.

Given the importance of spectral analysis of lattice quantum field theory data, the advancement of techniques for the same remains critically important. Therefore, we propose an algorithm that uses the first three time slices of the correlation function matrix to construct the transfer matrix and extract its energy eigenvalues. Reduction of systematic error arising from truncating the operator basis is achieved by varying the operator subspace dimension and applying eigenvalue-variance extrapolation. Since the correlation functions in early time slices typically exhibit small statistical errors and retain a strong signal of higher-excited states, we expect our proposed method to perform well in extracting higher-excited-state energies. In this paper, we conduct two lattice Monte Carlo simulations for quantum mechanical systems, harmonic and anharmonic oscillators, to evaluate the efficiency of our proposed method for higher-excited-state energies. We compare the energy levels obtained using the standard GEVP method and our proposed method. We find that our method consistently outperforms the standard GEVP method in extracting intermediate excited states for both systems. Because our method has access only to the first three time slices, it is not preferable to the GEVP method for extracting the ground-state energy in its current form.

In this work we predict the masses and binding energies of two $B_s$ exotic-meson candidates using Lattice QCD, namely the $B_{s0}^*$ and $B_{s1}$. We use a relativistic heavy-quark action for the valence b-quark in our simulations, tuned fully non-perturbatively by a neural network. This allows us to take the continuum limit and eliminates the largest systematic we attributed to our previous determination of these states using Lattice-NRQCD. This is the first Lattice QCD study to show that these states remain deeply bound in the continuum limit. We thoroughly benchmark our heavy-quark approach by reproducing the experimental values of the 1S hyperfine splittings of $B$ and $B_s$ mesons, as well as the mass splitting between the $B$ and $B_s$ mesons. Our final results yield binding energies with respect to the $BK$ and $B^*K$ thresholds of $-65.9(6.0)(3.0)_\text{Iso}$ MeV and $-60.6(6.6)(3.0)_\text{Iso}(1.0)_\text{GEVP}$ MeV for the $B_{s0}^*$ and $B_{s1}$ respectively.

We investigate the spin-dependent electromagnetic polarizabilities of the heavy vector mesons \(D^*\) and \(B^*\) in heavy meson chiral perturbation theory up to \(\mathcal O(p^3)\). Using a twelve-element tensor basis for the real-photon Compton scattering on a spin-1 target, we determine two scalar, four vector and six tensor polarizabilities. We take the charm- and bottom-sector axial couplings from the measured \(D^*\) width and lattice-QCD calculations, respectively, and estimate the magnetic couplings in the nonrelativistic constituent-quark model. In the charm sector, the proximity of the charged \(D\pi\) thresholds generates strongly nonanalytic \(P\phi\)-loop contributions, producing large real contributions to several \(\bar D^{*0}\) polarizabilities and sizable imaginary parts for \(D^{*-}\), whose charged \(D\pi\) channel is open. The \(E1E1\)-type polarizabilities are enhanced much more strongly than their \(M1M1\)-type counterparts, consistent with the velocity suppression of the pion-cloud magnetic coupling. No analogous enhancement occurs for \(B^*\): the Born terms govern the magnetic polarizabilities, and the anomaly poles dominate the vector polarizabilities that receive no Born contribution. These results resolve the spin dependence of the \(D\pi\) threshold effect and provide benchmarks for future lattice-QCD studies.

Simulating real-time dynamics in lattice gauge theories (LGTs) is severely constrained by the circuit depth overhead of standard fermion-to-qubit mappings, which scale linearly or quadratically with system size. To overcome this depth-scaling bottleneck, we introduce the Hardware-Aware Lattice Optimization (HALO) compiler, an architecture executing global time-evolution in an immutable $\mathcal{O}(1)$ circuit depth per Trotter step. By natively mapping composite gauge links to hardware topologies, HALO achieves a $91.36\%$ reduction in entangling gate overhead compared to unoptimized Jordan-Wigner baselines, compressing a 16-qubit global step to 56 CNOTs and bypassing extensive $\mathcal{O}(N)$ scaling limits. We validate this compiler on IBM superconducting transmon processors by simulating the mesoscopic Quantum Link Model (QLM) truncation of the Schwinger model. Coupling $\mathcal{O}(1)$ compilation with Zero-Noise Extrapolation (ZNE), we track localized string rupture, extracting the dynamical crossover of pair creation at $t \approx 0.790$ with an $18.3 \pm 2.2\%$ rupture probability. Furthermore, we map the dynamical phase diagram, identifying the confinement phase boundary at $g_c = 1.0$. Finally, we introduce a scalable 2D unit-cell blueprint, paving a direct pathway toward the fault-tolerant simulation of two-dimensional Quantum Chromodynamics (QCD).

We study electromagnetic radiative corrections to neutron $\beta$ decay within chiral perturbation theory extended to include the $\Delta(1232)$ resonance as an explicit degree of freedom. Building on a previous analysis performed in the $\Delta$-less theory, we identify and compute additional loop contributions with intermediate $\Delta$ states at leading and next-to-leading order in the small-scale expansion, and match the results to the pionless effective field theory. We find that the convergence of the chiral expansion significantly improved in the $\Delta$-full calculation. The electromagnetic shift in the axial coupling is reduced by $25\%$ compared to the $\Delta$-less result. The correction remains at the percent level and is phenomenologically significant for the comparison between experimental extractions and lattice-QCD determinations of the nucleon axial charge. We also obtain a new $\Delta$-induced contribution to the weak magnetism term, which is an order of magnitude smaller than the pion-loop result and negligible for upcoming experiments.

We compute for the first time the subleading twist correction to the exclusive rare $b \to \left \{s, d \right \} \ell^{+} \ell^{-}$ decays from the three-particle $B$-meson distribution amplitude at next-to-leading order accuracy by employing the soft-collinear effective theory. This constitutes the last missing ingredient for the complete factorization analysis of the hadronic matrix element of the weak effective Hamiltonian at leading power in the heavy quark expansion. Incorporating further a variety of the next-to-next-to-leading-order QCD corrections to the spectator-scattering amplitude and the weak annihilation topology, we then present the improved field-theoretic predictions for phenomenologically interesting observables in the electroweak penguin $B \to \left \{K, \pi \right \} \ell^{+} \ell^{-}$ decays.

Entanglement spectra in gauge theories can encode both symmetry breaking and the organization of gauge sectors. In the two-flavor Schwinger model at vacuum angle $\theta=\pi$, we find that the joint Schmidt distribution $p_{Q_A,F_A}$, labeled by the subsystem gauge charge $Q_A$ and flavor imbalance $F_A$, reveals a cut-dependent gauge-sector hierarchy and a mass-induced flavor asymmetry: changing the staggered cut reorganizes the gauge-charge distribution $p_{Q_A}$, while mass imbalance breaks the $F_A\leftrightarrow-F_A$ symmetry of the conditional flavor distribution $p_{F_A|Q_A}$. Defining the combined weight $W_F^{(q)}=p_{q,+1}+p_{q,-1}$ and conditional polarization $\mathcal P_F^{(q)}=(p_{q,+1}-p_{q,-1})/W_F^{(q)}$, we find that changing the cut reverses the weight hierarchy, $W_F^{(-1)}>W_F^{(+1)}$ at unit-cell boundaries but $W_F^{(+1)}>W_F^{(-1)}$ at intra-cell cuts, while mass imbalance drives $\mathcal P_F^{(q)}$ away from zero with a $q$-dependent cut response. Symmetry resolution therefore separates gauge-sector ordering, sector weight, and flavor polarization that are mixed in the globally ordered entanglement spectrum.

Hamiltonian truncation offers a nonperturbative route to quantum field theory, yet its accuracy is limited by the rapid expansion of the truncated Hilbert space, which drives up computational cost. We tackle this bottleneck with a hybrid strategy that pairs classical and quantum algorithms: 1) we develop an efficient basis-generation scheme built on integer partitions; 2) we speed up the construction of the sparse Hamiltonian matrix using symmetry-aware algorithms; and 3) we explore quantum Krylov diagonalization as a route to the low-lying spectrum. Benchmarking against the free massive scalar and $\phi^4$ theories in two spacetime dimensions, we achieve substantial gains in the computational efficiency of Hamiltonian truncation and chart a path toward future quantum implementations.

In holography, four-dimensional confining gauge theories are often modelled by five-dimensional Einstein–scalar gravity by choosing a specific form of the scalar potential. In a large class of non-conformal theories, we show that a predictive structure emerges for the thermal confinement transition by generalising the gravitational dual to $D+1$ dimensions and using a $1/D$ expansion. These results are independent of the details of the scalar potential, hinting towards universality. The black brane geometry dual to the deconfined phase can be analytically constructed due to its effects being localised near the horizon at leading order. The solution does not exist below a minimal temperature $T_{\rm min}$ and the maximum possible supercooling in the transition $\epsilon_{\rm sc} = 1-T_{\rm min}/T_{\rm c}$ is generically suppressed by a factor of $1/D^2$. Remarkably, the maximum supercooling at the leading order is set by the speed of sound in the deconfined phase of the gauge theory at the critical temperature, $\epsilon_{\rm sc}=c_s^2(T_{\rm c})/2$. These predictions agree with explicit calculations in an exponential superpotential, improved holography, and the thermal transition in $\mathcal{N}=4$ super Yang–Mills on a sphere.

We investigate the topological properties of QCD across the finite temperature Roberge-Weiss transition, which is found for particular values of the imaginary baryon chemical potential. Our study is conducted for $N_f = 2+1+1$ QCD with physical quark masses, discretized via stout improved staggered fermions and considering mostly two different values of the compactifed dimension, $N_t = 8$ and $N_t = 10$. Results for $T_{RW}$ and for the associated universality class are consistent with those found in the $N_f = 2 + 1$ case with a slightly different discretization. The topological susceptibility appears to be practically constant for $T \lesssim T_{RW}$, then rapidly decaying for higher temperatures. The analysis of the fourth order cumulant of the topological charge distribution, $b_2$, reveals that it is compatible with the prediction of the Dilute Instanton Gas Approximation right after $T_{RW}$, showing thus a sharp transition, which is more similar to what observed in pure gauge theories rather than to full QCD along the standard thermal line, where instead a slower transition was observed in previous studies.

We present a proof-of-concept numerical study of the real-time topological rate at non-zero momentum in quenched lattice QCD at a temperature $T\simeq 1.24 \, T_c \simeq 360$ MeV, as an important step toward the determination of this quantity in full QCD. Our strategy, already applied to compute the sphaleron rate in pure Yang–Mills and in full QCD, extracts the rate from the resolution of an appropriate inverse problem, solved applying the Hansen–Lupo–Tantalo (HLT) method to the thermal Euclidean time-correlator of the topological charge density. This method requires to control three different limits: continuum limit, limit of vanishing smearing width used in the HLT inverse problem resolution, and limit of vanishing smoothing radius used in the topological charge density correlator computation. Our lattice calculation is based on the standard Wilson discretization for the gauge action, and on three gauge ensembles with up to $N_\tau=16$ temporal points to achieve a controlled continuum limit. In all cases we employed an aspect ratio $LT=4$, which allowed us to compute the topological rate up to momenta as large as $p/T \sim 10$.

We examine the configurationwise relation between the first Gribov horizon, defined by loss of positivity of the Faddeev-Popov operator, and Zwanziger's horizon function, which probes the inverse operator through background-dependent sources. The analysis focuses on whether the spectral directions associated with the onset of the Gribov horizon are necessarily accessible to the sources entering the horizon function, including situations in which the critical subspace is degenerate. This question is studied for radial SU(2) hedgehog backgrounds in three and four Euclidean dimensions, where angular symmetry constrains the source sector while the radial profile controls the ordering of Faddeev-Popov thresholds. Variational estimates and finite-volume calculations are used to characterize the threshold structure for smooth radial profiles. The regular-gauge BPST background is treated separately because of domain issues associated with zero-energy behavior and the horizon source in the full-space setting. The discussion is restricted to configurationwise spectral properties and does not address the statistical weighting of these backgrounds in the Yang-Mills functional integral.

We investigate particle production from classical fields, a phenomenon central to the pre-equilibrium dynamics of relativistic heavy-ion collisions and the reheating epoch of the early Universe. Using lattice $\lambda\phi^4$ theory as a proof of principle, we show that this problem is naturally amenable to quantum computation, providing a first-principles framework for nonequilibrium quantum-field dynamics beyond existing approximations. We perform simulations on small spatial lattices, exhausting our available classical computational resources while maintaining a direct mapping to future quantum-computing implementations. We find that particle production is accompanied by equilibration of observables, including the field expectation value, occupation-number distribution, and pressure. The observed equilibration persists for timescales several times longer than the initial equilibration time before the observables resume oscillatory behavior associated with quantum Poincaré recurrences. Our results establish a route toward first-principles studies of equilibration in nonequilibrium quantum field theory and provide insight into the search for the smallest possible locally equilibrated quark-gluon systems at hadron colliders.