CyberSec Research

We investigate the applicability of complex Langevin dynamics to the three-dimensional XY model at finite chemical potential. To assess correctness, we introduce a new diagnostic based on the configurational temperature (or configurational coupling) estimator, recently proposed as a thermodynamic consistency check. We compare this criterion with the established Nagata-Nishimura-Shimasaki drift-decay test across a range of couplings and chemical potentials. Our results show that complex Langevin dynamics yields reliable results in the ordered phase (large $\beta$), but fails in the disordered phase (small $\beta$), even when the sign problem is mild. The configurational estimator provides a clear and physics-driven reliability test that complements drift-based diagnostics. These findings establish the estimator as a practical tool for identifying incorrect convergence, and highlight its potential for broader applications in lattice field theories with complex actions.

We consider 331 composite Higgs model (CHM3) in which the Lagrangian of the strongly coupled sector is invariant with respect to global SU(3)_C \times SU(3)\times U(1)_6 symmetry that can originate from SU(6) subgroup of E_6 and contains the gauge group of the standard model (SM) as a subgroup. The breakdown of the approximate SU(3)\times U(1)_6 symmetry down to SU(2)_W\times U(1)_Y subgroup around the scale f\sim 10 TeV results in a set of pseudo--Nambu--Goldstone bosons (pNGBs) that, in particular, involves Higgs doublet. The generation of the masses of the SM fermions in the CHM3 is discussed. We argue that an approximate discrete Z_2 symmetry may give rise to tiny masses of the left-handed neutrinos and several composite fermions with masses 1-2 TeV. The lepton and baryon asymmetries can be generated within the CHM3 via the out--of equilibrium decays of extra Majorana particle into the Higgs doublet and these composite fermions.

We present a neural network wavefunction framework for solving non-Abelian lattice gauge theories in a continuous group representation. Using a combination of $SU(2)$ equivariant neural networks alongside an $SU(2)$ invariant, physics-inspired ansatz, we learn a parameterization of the ground state wavefunction of $SU(2)$ lattice gauge theory in 2+1 and 3+1 dimensions. Our method, performed in the Hamiltonian formulation, has a straightforward generalization to $SU(N)$. We benchmark our approach against a solely invariant ansatz by computing the ground state energy, demonstrating the need for bespoke gauge equivariant transformations. We evaluate the Creutz ratio and average Wilson loop, and obtain results in strong agreement with perturbative expansions. Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems, and in a way that avoids both the sign problem and any discretization of the gauge group.

The mass and width of the lightest scalar open-charm state listed in the Review of Particle Physics, the $D_0^\ast(2300)$, are in puzzling tension with predictions from unitarized chiral perturbation theory (UChPT) and lattice QCD, which favor a lighter state at around $2100$ MeV. However, to date, no direct experimental evidence for this lighter state exists. In an effort to facilitate a direct observation, we introduce angular asymmetries of $B\rightarrow D \pi \ell \nu$ decays that allow for a direct extraction of the $D\pi$ S-wave phase shift and discuss a novel measurement strategy for the Belle II experiment. We conduct a sensitivity study, finding that the Belle II experiment can determine the pole location with sufficient precision to firmly establish the $D_0^\ast(2100)$ using the currently available data set. We also investigate the possibility and necessary statistics of measuring the $D\pi$ isospin 1/2 scattering length with an accuracy sufficient to distinguish between the predictions from both UChPT and lattice QCD and the measurement by ALICE using femtoscopy.

Simulating out-of-equilibrium dynamics of quantum field theories in nature is challenging with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields involves a high boson-to-qubit encoding overhead. Furthermore, when mapping to qubits, the infinite-dimensional Hilbert space of bosons is necessarily truncated, with truncation errors that grow with energy and time. A qubit-based quantum computer, augmented with an active bosonic register, and with qubit, bosonic, and mixed qubit-boson quantum gates, offers a more powerful platform for simulating bosonic theories. We demonstrate this capability experimentally in a hybrid analog-digital trapped-ion quantum computer, where qubits are encoded in the internal states of the ions, and the bosons in the ions' motional states. Specifically, we simulate nonequilibrium dynamics of a (1+1)-dimensional Yukawa model, a simplified model of interacting nucleons and pions, and measure fermion- and boson-occupation-state probabilities. These dynamics populate high bosonic-field excitations starting from an empty state, and the experimental results capture well such high-occupation states. This simulation approaches the regime where classical methods become challenging, bypasses the need for a large qubit overhead, and removes truncation errors. Our results, therefore, open the way to achieving demonstrable quantum advantage in qubit-boson quantum computing.

We study the phase transitions of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice using the non-perturbative first principle Monte Carlo simulations. Here $J_1 < 0$ and $J_2 > 0$ are the nearest and next-to-nearest couplings, respectively. In particular, the values of $J_2/|J_1| = 0.20, 0.22, 0.23, 0.24, 0.3, 0.5, 0.8,$ and 1.0 are considered in our study. Based on the numerical outcomes, we find that the phase transitions for $J_2/|J_1| = 0.20, 0.22, 0.23,$ and 0.24 are second order and are governed by the 2D Ising universality class. In addition, we find evidence to support the facts that there are transitions for $J_2/|J_1| = 0.5, 0.8$ and 1.0 and these phase transitions are second order. Our results also indicate phase transition is unlikely to take place for $g=0.3$. We are not able to obtain results for $J_2/|J_1|$ $\in$ (0.24, 0.3) because the associated integrated autocorrelation times or (and) the equilibrium times are extremely large at the low-temperature region. A comparison between the outcomes presented here and the available results in the literature is briefly conducted as well.

We introduce a multigrid multilevel Monte Carlo method for stochastic trace estimation in lattice QCD based on orthogonal projections. This formulation extends the previously proposed oblique decomposition and it is assessed on three representative problems: the connected pseudoscalar correlator, the trace of the full Dirac operator's inverse $\mathrm{tr}(D^{-1})$, and disconnected fermion loops. For the connected correlator, variance reductions grow systematically with the time separation and lead to cost savings of up to a factor of 30 at large separations, outperforming both the plain Hutchinson's estimator and the oblique formulation. For $\mathrm{tr}(D^{-1})$, reductions are more modest but remain systematic, with stronger effects on more ill-conditioned systems. Disconnected loops show no improvement, since their variance is dominated by local same-slice contributions not targeted by the decomposition.

The onset of hydrodynamics in the hot medium created in relativistic heavy-ion collisions is a crucial theoretical question. A first-principle simulation requires a real-time, non-perturbative calculation of the quantum system. In this Letter, we perform such simulations using the tensor network method, which enables large-scale quantum many-body simulations by retaining only the most essential quantum states for collective behaviors. We focus on the massive Schwinger model, a low-dimensional analog of quantum chromodynamics (QCD), as they share important properties such as confinement and chiral symmetry breaking. Starting from an initial state that puts a localized excitation atop the vacuum and mimics the energy deposition from colliding nuclei, we observe hydrodynamic behavior consistent with Bjorken flow in all relevant degrees of freedom: energy density, fluid velocity, and bulk pressure. The time scale for hydrodynamic onset aligns with the thermalization time of the quantum distribution function.

We simulate the real-time dynamics of a massive Schwinger model using the Time-Evolving Block Decimation tensor network algorithm. Starting from a non-equilibrium initial state with localized energy excitation on top of vacuum, we track the subsequent evolution to investigate two distinct physical phenomena. First, by analyzing the system's energy-momentum tensor, we show that this system exhibits hydrodynamic behavior analogous to Bjorken flow at large coupling-to-mass ratio, a signature that diminishes as the coupling weakens, or mass increases. Second, by examining the evolution of the electric field and charge density, we observe the signal of spontaneous parity symmetry breaking phase transition in a dynamical system. The parity-restored regime is marked by ''string breaking'' and efficient charge screening, while the parity-broken regime displays stable propagation of nearly free charges and persistent electric fields connecting them.

We demonstrate that the leading IR-renormalon divergence in the perturbative pole mass of a massive quark resides entirely in the contribution from the trace anomaly of the energy-momentum tensor in QCD. Consequently, the recently proposed trace-anomaly-subtracted $\sigma$-mass definition for heavy quarks is not only scheme- and scale-invariant, but also free from the leading IR-renormalon ambiguity. We further derive a formula connecting this $\sigma$-mass to the perturbative pole mass, solely in terms of the QCD $\beta$-function, quark-mass anomalous dimension $\gamma_m$ and a proper rewritten form of the pole-to-$\overline{\mathrm{MS}}$ mass conversion factor. Utilizing this formula along with the ingredients available in the literature, we present the explicit five-loop result for the perturbative relationship between the $\sigma$-mass and the perturbative pole mass in QCD under the approximation of keeping only a single quark massive. Given the theoretical merits of this mass definition and the availability of high-precision conversion relations, we encourage its application to high-energy processes with heavy quarks, e.g., $H \rightarrow b\bar{b} + X_{\mathrm{QCD}}$, and to current-current correlators used in determining heavy-quark masses and decay widths.

While we have several complementary models of confinement, some of which are phenomenologically appealing, we do not have the ability to calculate analytically even simple aspects of confinement, let alone have a framework to eventually prove confinement. The problem we are facing is to evolve the theory from the perturbative regime to the long distance confining regime. This is generally achieved by renormalization group transformations. With the gradient flow we now have a technique to address the problem from first principles. The primary focus is on the running coupling $\alpha_S(\mu)$, from which confinement can be concluded alone. A central point is that the gluon condensate is scale invariant, which reflects its self-similar behavior across different scales. Building on that, we derive $\alpha_S(\mu) \simeq \Lambda_S^2/\mu^2$, which evolves to the infrared fixed point $1/\alpha_S = 0$ in accordance with infrared slavery. This shows that the only important factor is the presence of homogeneous vacuum fields, represented by condensates, which is a universal feature that QCD shares with many other models. The analytical statements are supported by numerical simulations.

We present spectral functions extracted from Euclidean-time correlation functions using sparse modeling (SpM). SpM solves inverse problems by considering only the sparsity of the target solution. To assess the applicability of the method, we first test it with mock data that mimic charmonium correlation functions. We show that, while resonance peaks in the spectral functions can be reconstructed using this method, it is difficult to reconstruct transport peaks without further assumptions beyond SpM. Then we extract charmonium spectral functions from correlation functions obtained from lattice QCD at temperatures below and above the critical temperature. We show that this method yields results qualitatively consistent with those obtained using the maximum entropy method, although the transport peak is not obtained clearly. This suggests that the results solely from the assumption of the sparse solution can partially reflect underlying physics.

Linear systems arise in generating samples and in calculating observables in lattice quantum chromodynamics~(QCD). Solving the Hermitian positive definite systems, which are sparse but ill-conditioned, involves using iterative methods, such as Conjugate Gradient (CG), which are time-consuming and computationally expensive. Preconditioners can effectively accelerate this process, with the state-of-the-art being multigrid preconditioners. However, constructing useful preconditioners can be challenging, adding additional computational overhead, especially in large linear systems. We propose a framework, leveraging operator learning techniques, to construct linear maps as effective preconditioners. The method in this work does not rely on explicit matrices from either the original linear systems or the produced preconditioners, allowing efficient model training and application in the CG solver. In the context of the Schwinger model U(1) gauge theory in 1+1 spacetime dimensions with two degenerate-mass fermions), this preconditioning scheme effectively decreases the condition number of the linear systems and approximately halves the number of iterations required for convergence in relevant parameter ranges. We further demonstrate the framework learns a general mapping dependent on the lattice structure which leads to zero-shot learning ability for the Dirac operators constructed from gauge field configurations of different sizes.

We calculate the Casimir energy for the configuration of two parallel plates coupled to nonabelian gauge fields with a Yang-Mills action. We consider both 2+1 and 3+1 dimensions in the manifestly gauge-invariant formalism we have pursued over the last several years which allows us to factor out the gauge degrees of freedom. A boundary action in the functional integral, equivalent to the insertion of operators representing the plates, is used to enforce the required boundary conditions for the gauge fields. The result is for a kinematic regime corresponding to the exchange of gluons with a dynamically generated mass. We find good agreement in 2+1 dimensions and reasonable agreement in 3+1 dimensions with lattice-based numerical evaluations.

We present a light-cone QCD sum rule analysis of the semileptonic decays of $\Xi_c$ baryons, focusing on the channels $\Xi_c^0 \to \Xi^- \ell^+ \nu_\ell$, and $\Xi_c^+ \to \Xi^0 \ell^+ \nu_\ell$. The transition form factors are calculated within the light-cone QCD sum rules framework, using the distribution amplitudes of the heavy $\Xi_c$ baryons. The obtained form factors are then used to compute the differential and total decay widths, as well as the branching fractions. Our numerical results for the branching fractions are $\mathcal{B}(\Xi_c^0 \to \Xi^- \ell^+ \nu_\ell) = (3.73 \pm 1.04)~\%$ , $\mathcal{B}(\Xi_c^0 \to \Xi^- \mu^+ \nu_\mu) = (3.59 \pm 1.01)~\%$, $\mathcal{B}(\Xi_c^+ \to \Xi^0 \ell^+ \nu_\ell) = (11.2 \pm 3.25)~\%$, and $\mathcal{B}(\Xi_c^+ \to \Xi^0 \mu^+ \nu_\mu) = (10.8 \pm 3.13)~\%$. These results are in good agreement with recent lattice QCD calculations, while being larger than the current experimental measurements and differing from the predictions of other theoretical approaches.

We investigate theoretical signatures of first-order QCD phase transitions in high-density astrophysical systems through a framework combining lattice QCD, effective field theories, and multimessenger constraints. Hybrid equations of state with Maxwell and Gibbs constructions, constrained by lattice QCD at finite temperature and baryon chemical potential up to mu_B/T < 3, interpolate consistently between chiral effective field theory at nuclear densities and perturbative QCD at asymptotic densities. Applying these models to static neutron stars via Tolman-Oppenheimer-Volkoff equations and to binary mergers via relativistic hydrodynamics, we find distinctive signatures: (i) twin star branches with 0.5-2.0 km radius differences at fixed mass, (ii) equation of state softening in coexistence regions reducing maximum masses by 0.2-0.4 solar masses, (iii) delayed post-merger gravitational-wave frequency shifts of 200-400 Hz, and (iv) enhanced neutrino emission during phase transitions. Confronted with multimessenger constraints from GW170817, NICER observations of PSR J0740+6620 and PSR J0030+0451, and perturbative QCD, our models suggest strong first-order transitions are marginally consistent with current data but produce signatures detectable by next-generation detectors. Neutron star core sound speeds satisfy c_s^2 < 0.5c^2, with transient conformal bound violations in 2-4 times saturation density. This framework yields quantitative predictions for the Einstein Telescope and Cosmic Explorer, establishing foundations for precision QCD matter tests and possible quark matter discovery.

It is well-known that the standard instanton analysis in 4d Yang-Mills is plagued with the instanton size moduli problem, which renders the instanton contribution to vacuum energy density (or one-instanton partition function) infrared divergent. The formalism also ignores the implications of long range (magnetic dipole type) $1/r^4$ interaction between the small instantons, since it is weaker than Coulomb interaction. We show that in $U(1)$ lattice gauge theory, where finite action configurations are monopole loops, small loops at large separations also interact with the same type of $1/r^4$ interaction. If one ignores the classical interactions between monopoles, following the same idea as in Yang-Mills theory, the one-monopole partition function is also infrared divergent at strong coupling. However, $1/r^4$ interactions among small loops should be viewed as a consequence of multipole expansion, and emanate from $1/r^2$ interaction between current segments. Taking interactions into account, one can prove that the strongly coupled $U(1)$ lattice gauge theory is dual to a lattice abelian Higgs model, and more importantly, free of infrared divergences. The model exhibits mass gap and confinement by monopole condensation. We suggest that the structure of moduli space of instantons, ADHM data, and the long ranged classical interactions in pure Yang-Mills theory should be examined with this refined perspective. We conjecture that, in contradistinction to the current views on the subject, internal structure of instantons in Yang-Mills theory is responsible for confinement in $4d$ , similar to sigma model in $d=2$ dimensions.

We show that the lattice glueball masses $M_G$ versus $N$ in SU($N$) and Sp($2N$) Yang-Mills theories scale as $\frac{M_G}{\sqrt\sigma}\sim \sqrt{\frac{C_2(adj)}{C_2(f)}}$, with $\sigma$ the fundamental string tension and $C_2(adj)$ and $C_2(f)$ the quadratic Casimir of the gauge algebra in the adjoint and fundamental representations. This scaling behaviour is followed by the great majority of available lattice glueball states, and may set constraints on $SU(3)$ models by imposing a specific behaviour at $N\neq 3$. The observed scaling is compatible with two assumptions: (1) The glueball masses are proportional to the square root of the adjoint string tension, $M_G\sim \sqrt\sigma_{adj}$; (2) The string tension follows the Casimir scaling, i.e. $\sigma_{adj}=\frac{C_2(adj)}{C_2(f)}\sigma$. In a constituent gluon picture, our results suggest a low-lying glueball spectrum made of two transverse constituent gluons bound by an adjoint string, completed by three transverse constituent gluons bound by a Y-junction of adjoint strings rather than a $\Delta-$shaped junction of fundamental strings.