Papers

We compute the equation of state of dense and magnetized strongly interacting matter using lattice QCD at a non-zero value of the lattice spacing. Our simulations employ $2+1+1$ dynamical flavors of rooted staggered quarks with masses tuned to the physical point. To conform with experimental constraints, we impose strangeness neutrality and isospin asymmetry on our observables. We circumvent the sign problem by simulating imaginary values of the chemical potential and applying the $T'$-expansion scheme to carry out the analytic continuation of our observables to the real chemical potential axis. This novel scheme, adapted to the setup with nonzero magnetic fields, is demonstrated to produce significantly smaller systematic errors in the final observables, compared to the standard analytical continuation at fixed temperature, allowing for better-controlled extrapolations. Our results for the pressure, the entropy density and the interaction measure are tabulated for direct use in heavy-ion phenomenology applications.

The Wess-Zumino-Witten interaction in chiral perturbation theory is a manifestation of chiral anomalies. One of its consequences is the presence of a nonvanishing $K \overline K \to \pi^+ \pi^0 \pi^-$ amplitude. We derive the finite-volume formalism that allows one to access this, and related, amplitudes, using the spectra of two and three particles in finite volumes, spectra that can be calculated using lattice QCD. Specifically, we present the formalism for the systems $K \overline K + 3 \pi$ with $I=0$ and $\pi K + \pi\pi K$ with $I=1/2$ and $3/2$. In addition, we determine the threshold expansions for the $2\leftrightarrow 3$ and $3\leftrightarrow 3$ K matrices that enter the formalism, and calculate the leading order predictions from chiral perturbation theory for the coefficients that enter these expansions.

In this work, we systematically investigate the baryon-baryon interactions in singly bottomed dibaryon systems within the chiral quark model and search for possible bound states. By exploring the baryon-baryon interaction, we find that low-isospin channels tend to generate deeper attractive interactions and are prone to form bound states. We also find that decuplet-decuplet systems tend to show stronger attraction and support a larger number of bound states, whereas octet-octet systems generally exhibit weaker attraction and fewer bound solutions. The binding behavior of octet-decuplet systems generall lies between these two cases. Several bound states are obtained, which are $\Delta\Sigma_b^*$ with $IJ=\frac{1}{2}0$, $\frac{1}{2}1$, $\frac{1}{2}2$, $\frac{1}{2}3$, and $\frac{3}{2}3$, the $\Delta\Sigma_b$ with $IJ=\frac{1}{2}1$, $\frac{1}{2}2$, $\frac{3}{2}1$, and $\frac{3}{2}2$, the $N\Sigma_b^*$ with $IJ=\frac{1}{2}2$, the $\Sigma\Sigma_b$ with $IJ=00$, $01$, and $11$, the $\Sigma\Sigma_b^*$ with $IJ=01$ and $02$, the $\Sigma^*\Sigma_b$ with $IJ=01$ and $02$, and the $\Sigma^*\Sigma_b^*$ with $IJ=00$, $01$, $02$, $03$, and $13$. Further investigations of the corresponding scattering processes are still required to determine whether these bound-state candidates can be identified. These states deserve further experimental investigation.

This work provides a digital quantum simulation scheme for $1{+}1$-dimensional $SU(2)$ Yang–Mills theory with Dirac fermions. It takes the form of a quantum circuit, infinitely repeating across space and time with $\Delta_t=\Delta_x=\varepsilon$, whose wires follow lightlike propagation. The construction mirrors the logic of the standard quantum field theory approach, transposed to the discrete setting. Namely, we start from the Dirac quantum walk, restore $SU(2)$ gauge symmetry by introducing the gauge field, lift the walk to a multi-particle QCA while preserving fermionic anticommutation, and equip the gauge field with its own dynamics. Rather than relying on Clebsch–Gordan decompositions, we use the pointwise-product structure of gauge-link updates, which yields self-contained proofs of unitarity and gauge covariance in quantum-computing notation. The construction provides an explicit algorithmic formulation of the theory, whose continuum limit we discuss.

We present the first QCD determination of an energy-dependent form factor for a two-hadron scattering state. In particular, we calculate the QCD contribution to the forward electromagnetic $\pi^+\pi^+ + \gamma\to\pi^+\pi^+$ amplitude at $m_\pi\approx 400$~MeV using lattice QCD. Because lattice calculations are performed in a finite Euclidean spacetime, where asymptotic scattering states are absent, this amplitude cannot be accessed directly from correlation functions. Instead, we can constrain this and related amplitudes nonperturbatively using a finite-volume formalism that requires two ingredients: the discrete finite-volume spectrum and finite-volume matrix elements of the electromagnetic current. We calculate three-point correlation functions coupling $\pi^+\pi^+$ finite-volume states and extract the corresponding electromagnetic matrix elements. Combining these results with the previously determined spectrum, we constrain the infinite-volume $\pi^+\pi^+ + \gamma\to\pi^+\pi^+$ amplitude in the forward limit. Using constraints from Lorentz symmetry, unitarity, and analyticity, we describe this amplitude in terms of a single real-valued energy-dependent two-hadron form factor. The resulting amplitude and form factor agree with the Ward-Takahashi identity across all energies and moving frames considered, providing the first QCD validation of this finite-volume approach and a pathway toward first-principles studies of the electromagnetic structure and electroweak responses of resonances and multi-hadron bound states.

We present lattice QCD results for the CP violating pion-nucleon coupling $\bar{g}_0$ induced by the QCD $\overline\Theta$ term from the analysis of three 2+1+1-flavor ensembles generated with highly improved staggered quarks (HISQ) by the MILC collaboration. These ensembles are at lattice spacing $a\approx 0.09~\text{fm}$ and pion masses of 313, 226 and 138 MeV, respectively. The coupling $\bar{g}_0$ is extracted in two ways. First, from the matrix element of the correlation between the pesudoscalar current and the topological charge evaluated between the nucleon ground state. The data for correlation functions with both the pseudoscalar and axial vector exhibit large contamination from the $N\pi$ excited state. We show that these can be controlled at the leading order using chiral perturbation theory ($\chi$PT) and the axial Ward identity (AWI, also called the partially conserved axial current (PCAC) relation). The result after removing the $N\pi$ contamination and extrapolating to the physical pion mass is, however, noisy: $\bar{g}_0/(2F_\pi)=-7(63)\times 10^{-3} \,{\overline{\Theta}}$. The more precise result $\bar{g}_0/(2F_\pi)=17.4(1.9)\times 10^{-3} \,{\overline{\Theta}}$ is obtained using low energy effective field theory methods or equivalently the AWI. Since contamination from the $N\pi$ excited states arises in the calculation of many nucleon matrix elements, we give an extended discussion on them and the use of the AWI for controlling them in the calculation of $\bar g_0$.

Open-system lattice gauge theory (LGT) has so far been developed predominantly in Abelian settings, leaving open how genuinely non-Abelian gauge structure reshapes dissipative real-time dynamics. Here, we study a $1+1$D SU(2) Yang–Mills LGT with dynamical matter coupled to a thermal scalar environment through a gauge-preserving Lindblad evolution, which we solve using tensor networks. Starting from a quark–antiquark pair connected by a chromoelectric flux string, we find that the thermal medium melts the string by delocalizing the color charges and screening the flux; on resonance, this dissipative melting competes with and delays coherent string breaking. The thermalization time is non-monotonic in the environment coupling, decreasing through environment-assisted transport at weak dissipation before increasing in a quantum-Zeno regime. In the strong-dephasing limit, a Schrieffer–Wolff expansion maps the dynamics to a classical exclusion process and yields the Liouvillian thermalization time analytically. Beyond these generic open-system effects, the non-Abelian matter structure produces a systematic mesonic bias in the steady state, while the thermalization time decreases with temperature, in contrast to the Abelian Schwinger model trend and in qualitative agreement with pNRQCD studies of the quark–gluon plasma. These results establish a gauge-preserving framework for thermalization and string dynamics in open non-Abelian lattice gauge theories.

Understanding real-time string dynamics in three spatial dimensions is essential for connecting quantum simulations of lattice gauge theories (LGTs) to the physical dimensionality of QED and QCD, where transverse fluctuations and competing local processes proliferate. We present the first real-time simulations of string breaking in $3+1$D lattice quantum electrodynamics. Using tree tensor networks, we simulate the quench dynamics of electric flux strings in a $3\!+\!1$D U(1) LGT with dynamical matter. At strong coupling, the string breaks resonantly at a sharp resonance condition of mass and gauge couplings, converting electric energy into matter–antimatter pairs that screen the static charges. Off resonance, we classify all competing channels—pair production, string deformations and extensions, and flux loops—whose multiplicity, extensive for pair production and flux loops, depletes the string sector even far from resonance. A channel-resolved perturbation theory quantitatively reproduces these dynamics and their Fourier spectrum. Our results establish diagnostics and benchmarks for upcoming quantum simulators of higher-dimensional LGTs.

We develop a continuum framework for comparing the Gribov–Zwanziger and center-vortex descriptions of confinement through the gauge-invariant twisted partition function of the electric $\mathbb{Z}_N^{[1]}$ 1-form symmetry. A background 2-form field $B$, equivalently an 't~Hooft twist on a torus, labels a global sector and is not itself a dynamical center vortex. For a minimal irreducible twist on $T^4$, we derive the complete adjoint momentum lattice of $SU(N)$. The twisted spectrum is exactly the scalar spectrum on an enlarged torus with periods $(L_1,L_2,NL_3,NL_4)$ with the ordinary-torus sublattice removed. This yields a finite Faddeev–Popov gap at the flat representative and reduces twisted-minus-untwisted spectral traces to ordinary torus traces. For the refined Gribov–Zwanziger (RGZ) kernel, Poisson resummation gives an exact finite-volume Bessel-function winding sum with a universal center-twist projector. We evaluate the Gaussian one-loop integral at fixed RGZ parameters up to the finite-dimensional global zero-mode/stabilizer normalization. The Zwanziger determinants cancel, while the gauge-fixing/ghost sector leaves a universal massless primed determinant on $T^4$; the untwisted sector also contains constant gluon modes. The only normalization not fixed by the local quadratic Hessian is the relative zero-mode/stabilizer measure of the reducible untwisted and irreducibly twisted flat connections. We also derive closed finite-volume sources for the RGZ stationary equations. The massive response is exponentially suppressed at large volume, whereas the massless factor depends on the global zero-mode normalization. Thus the Gaussian calculation does not by itself establish the strong center-vortex-condensation criterion for $Z[B]/Z[0]$, but it isolates the remaining global normalization problem and separates a global twist from an actual dynamical vortex.

The "left-hand cut problem" in lattice QCD arises when exchange singularities invalidate standard relations used to extract scattering amplitudes from the finite-volume spectrum. In recent years, several approaches were proposed to resolve this problem. We establish analytically and verify numerically the equivalence between the three-body approach proposed in [JHEP 06 (2024) 051] and the two-body left-hand cut formalism developed in [JHEP 08 (2024) 075]. We test the equivalence in a scalar model describing a particle scattering from an $S$-wave two-particle bound state through one-particle exchange. Both approaches reproduce the same infinite-volume particle–bound-state amplitude and correctly encode the associated left-hand cut in the finite-volume spectrum. Crucially, we identify that the exponentially suppressed finite-volume effects neglected in both formalisms can be numerically large, compromising amplitude extraction at small lattice volumes.

To make full use of the HL-LHC, especially in the search for BSM physics, all Standard Model backgrounds have to be understood with increased precision. This is especially difficult for Double Parton Interactions (DPIs) and more generally Multi Parton Interactions (MPIs), which are very difficult to isolate precisely in experiment. DPIs are parameterized by Double Parton Distributions (DPDs) and the lattice determination of the latter is, therefore, especially attractive. In our previous work on DPDs on the lattice, we focused on the results obtained from one gauge ensemble with higher than physical pion mass. In this work, we extend our efforts by investigating artifacts introduced by finite volume and the dependence on the lattice spacing. Moreover, we consider the dependence on the mass parameters. This study is carried out by employing the Wilson-Clover fermion gauge ensembles generated by the CLS collaboration.

Spin models with a given symmetry are easier to sample than scalar theories with the same symmetry on a lattice, as the constrained nature of spin variables enables cheap heat-bath updates. However, this constraint suppresses radial fluctuations, and consequently, spin models cannot be used to study the phenomena of spontaneous symmetry breaking, such as the Higgs phenomenon. To address this, we propose a class of scalar potentials based on Gaussian Mixture Models (GMMs) that are as easy to sample as spin models with a given symmetry. These potentials can be designed to belong to the same universality class as the theory of interest, thereby reproducing its critical properties while enabling efficient sampling. We construct such models for global $\mathbb{Z}_2$ symmetry, $U(1)$ gauge symmetry, and disordered systems. We also verify by numerical experiment that the case of $\mathbb{Z}_2$ symmetry in two dimensions lies in the two-dimensional Ising universality class.

A broad class of physical observables can be expressed in terms of smeared spectral functions. Important examples include the hadronic vacuum polarization contribution to the muon $g-2$, hadronic $\tau$ decays, inclusive semileptonic $B$ and $D$ decays, and amplitudes for rare processes such as $B\to K^{(*)}\ell^+\ell^-$. In recent years, a variety of methods have been proposed to reconstruct or constrain such spectral functions from Euclidean correlators and related inputs. However, the inverse problem is intrinsically ill-posed, making it difficult to obtain fully reliable, model-independent results with controlled uncertainties. In this contribution, I summarize recent developments, discuss the opportunities offered by smeared spectral observables, and highlight the main challenges that remain.

We construct a dispersive representation of the relativistic $3\to 3$ scattering amplitude for three identical spinless particles in the $S$-wave. The two-particle subenergy, instead of the total energy, is used as the dispersive variable. This choice keeps the physical dispersive contour free of the kinematical cuts that complicate total-energy dispersion relations. By separating discontinuities across the two-particle subenergy cuts from that across the three-body cut, we derive a linear integral equation with one-particle exchange as the driving term. We further show that the solution satisfies three-body unitarity as a consequence of two-body unitarity, analyticity, and crossing symmetry. For pair-wise interactions, this representation can be rewritten into the form used for isobar-spectator scattering. Finally, we give prescriptions for contour deformation and the subtraction of poles in the two-body subsystem amplitudes, which continue the amplitude onto adjacent unphysical Riemann sheets and thus provide direct access to the analytic structure relevant for three-body resonance poles.

The strong $CP$ problem remains one of the major open questions in the Standard Model of particle physics. Its best-known solution is the Peccei–Quinn mechanism, which predicts a new pseudoscalar boson, the QCD axion. In recent years, alternative solutions and new perspectives on the foundations of the strong $CP$ problem have also received renewed attention. In this review, we provide a pedagogical account of the underlying physics and summarise the current theoretical and phenomenological status of the problem.

A three-matrix model that contains a plethora of fuzzy sphere solutions was defined twenty years ago. It has been shown that in a certain regime of the model, combinations of fuzzy spheres become classical solutions of the model. In the original paper and subsequent works, the stability of specific states has been discussed, showing that only a single largest fuzzy-sphere configuration is stable. Here, we focus on a complementary question: starting from some initial configuration, is the thermodynamically preferred state approached rapidly, or are there other long-lived, metastable configurations which may support interesting physics? We find that the answer in the large-matrix limit depends on the dispersion of the initial configuration. We identify the elementary transition as an accretion, in which one sphere absorbs a single unit from another, and show that it is driven by fluctuations of the sphere centers. By measuring these fluctuations in long simulations, we find quantitative agreement with the one-loop effective action, with no free parameters. For multi-sphere states, we find that the stiffness of an inner sphere grows logarithmically with the number of surrounding layers, so that concentric onion-like configurations – describing an emergent three-dimensional quantum space – become increasingly long-lived.

We present $SU(3)$ lattice gauge theory results for the $\mathcal{O}(1/m_Q)$ hybrid spin-dependent and hybrid-quarkonium mixing potentials. The only existing lattice computation of these potentials is limited to quark-antiquark separations smaller than approximately $0.5\,\text{fm}$. In this work, we extend the lattice results up to around $1.25 \, \text{fm}$ using large-volume, high-statistics simulations at several lattice spacings and gradient flow times, providing the first lattice data in this previously unexplored regime.

We investigate the dissociation of the neutral pion in hot magnetized quark matter within the two-flavor Nambu–Jona-Lasinio model. At zero magnetic field, the Mott temperature is conventionally determined by $m_{\pi^0}(T_{\rm Mott})=2M(T_{\rm Mott})$, above which a real pole ceases to exist. At finite magnetic field, Landau quantization replaces this single threshold by a hierarchy of quark–antiquark continua and generates multiple solutions of the pion pole equation, rendering a direct threshold-crossing criterion ambiguous since a real pion solution below the lowest nominal threshold always exists. We therefore propose to define the magnetic Mott temperature through the inflection point of the pion wave-function renormalization factor $Z_{\pi^0}(T,eB)$ of that lowest pole, corresponding to the fastest loss of its spectral function strength. The prescription reproduces the conventional Mott temperature as $eB\to 0$ and tracks the chiral pseudocritical temperature for both constant and magnetic-field-dependent couplings. Our results characterize pion dissociation in a magnetic field as a spectral crossover rather than a simple threshold crossing.

The two-photon decay of the neutral pion is fixed in the chiral limit by the Adler-Bell-Jackiw anomaly, while nonzero quark masses induce few-percent corrections that must be determined for precision tests of QCD beyond the chiral limit. Using the anomalous PCAC relation, we compute them in lattice QCD as deviations from the exact anomaly condition at $q^2=0$, thereby avoiding both four-point functions and the cancellation of chiral logarithms that limits conventional approaches. Because the correction is proportional to the light-quark masses, both statistical and systematic uncertainties are correspondingly suppressed, making a precision calculation feasible. On two nearly-physical domain-wall ensembles we achieve $\sim1\%$ statistical precision each for the decay width, obtaining $\Gamma(\pi^0\to\gamma\gamma)=8.09(22) eV$ after continuum extrapolation. The $2.3(1.4)\%$ mass correction to the decay amplitude, positive and isospin-breaking dominated, provides the first ab initio confirmation of the $\pi^0$-$\eta$-$\eta'$ mixing enhancement.

We present part one of an SU(3)-flavour-symmetric lattice QCD calculation of the amplitude for a $D$-meson decaying to a $K\pi$ final state in the 27-dimensional irreducible representation of the flavour symmetry group, denoted $(K\pi)_{\mathbf{27}}$. The Wilson–clover gauge ensembles used in this work, generated by the OpenLat collaboration, are tuned such that $M_\pi = M_K \approx 410\,\mathrm{MeV}$. Using the distillation framework, we construct a matrix of Euclidean correlation functions from pairs of single-hadron operators projected to definite spatial momentum. Solving a generalised eigenvalue problem yields the finite-volume energy spectrum that is used to determine the scattering phase shift from threshold up to $4 M_\pi \approx 1640 \,\mathrm{MeV}$, which sits below but plausibly within reach of $M_D^{\rm SU(3)} \simeq 1900\,\mathrm{MeV}$. The calculation is performed across three lattice spacings, and we apply two strategies in which the continuum limit is taken at different stages of the computation: (i) on the extracted scattering parameters and (ii) on the finite-volume energies at fixed physical volume before extracting the scattering parameters. We find consistent results across these methods for the scattering phase shift as a function of the centre-of-mass energy, $\delta_{\mathbf{27}}(E_{\sf cm})$. Taking a scattering-length-only parametrisation, we infer a value for the strong phase of the weak decay, $\delta_{\mathbf{27}}(M_D^{\rm SU(3)})=-38.4(2.4)^\circ$. We further describe the methodology for using the same operator basis to compute three-point correlation functions to extract $\langle (K\pi)_{\mathbf{27}}| H_W| D\rangle$, for the tree-level effective weak Hamiltonian $H_W$, and for relating such finite-volume matrix elements to the full decay amplitude. The complete analysis leading to the latter will be presented in a forthcoming manuscript.

First, we explicitly construct zero-modes of the Yang-Mills Faddeev-Popov operator in the presence of two parallel plates, with either perfect electric (PEC) or perfect magnetic (PMC) boundary conditions imposed. This establishes the existence of Gribov copies with finite action, and even finite L_2-norm, in Yang-Mills theory with non-trivial interfaces. We adapt Henyey's construction, although the boundary configuration imposes extra restrictions on the ansatz for the gauge field. Second, we discuss the phenomenon of an emergent boundary gauge invariance for PEC and PMC plates in Yang-Mills theory. This shall be important when applying the Gribov-Zwanziger procedure to parallel plate setups, of relevance for non-perturbatively studying the non-Abelian Casimir effect in the future.

We investigate meson gravitational D-form factors in the three-flavor linear sigma model and their connection to symmetry breaking in low-energy QCD. Within the scalar meson dominance picture, we examine the scalar meson exchange contributions and their relation to meson masses through scalar-meson couplings. In the three-flavor symmetric limit, we first derive analytical expressions for the D-form factors of pseudoscalar and scalar mesons. In the chiral limit, the forward-limit value of the octet pseudoscalar D-form factor is fixed to $-1$, whereas the $U(1)_A$ anomaly generates additional contributions to the singlet pseudoscalar and scalar-meson D-form factors. For realistic flavor breaking, the interaction introduced to reproduce the scalar-meson mass hierarchy below $1$ GeV significantly affects the scalar-meson D-form factors. We further compare the linear sigma model results with those obtained from a chiral perturbation theory Lagrangian including a dilatonic scalar field and show that their differences are governed by the canonical mass dimensions of the interaction terms contributing to meson mass generation. These results indicate that meson D-form factors provide sensitive probes of symmetry-breaking structures in low-energy hadron physics.

We present a retrospective case study of bias-corrected machine learning (ML) estimates of traces of the inverse Dirac operator, $\text{Tr}\,M^{-n}$ ($n=1,2,3,4$), using a fixed lattice QCD dataset and examining how the results depend on the relative proportions of the labeled and training sets. Two supervised learning approaches are examined: one using $\text{Tr}\,M^{-1}$ as the input feature, and the other employing gauge observables such as the plaquette and rectangle. Beyond the direct estimation of $\text{Tr}\,M^{-n}$, we further investigate two derived applications of the ML estimations: the evaluation of the cumulants of the chiral condensate within a single ensemble and that obtained through multi-ensemble reweighting across ensembles with different quark masses. Within this fixed dataset, the bias-corrected estimates show close agreement with the full-data reference under the adopted evaluation criteria, while the uncorrected estimates can exhibit amplified deviations after the nonlinear cumulant and reweighting steps. For the approach using $\text{Tr}\,M^{-1}$ as the input feature, nominal solve-count accounting suggests that the Dirac-inversion cost could be reduced to approximately $25.75\%$ of that of the conventional calculation in the present setup. This value is a cost projection rather than an end-to-end benchmark: it assumes comparable costs for successive inversions and excludes model-training and analysis overhead.

We introduce a two-coupling generalization of $\mathbb{C}P^{N-1}$ model that continuously interpolates between the self-dual ($\epsilon=0$) and the physical ($\epsilon=g$) theories as a useful nonperturbative tool. At $\epsilon \neq g$, this model possesses a chiral imbalance, which may be viewed as a real topological deformation (imaginary-$\theta$). We demonstrate that exact quantum equivalence between first- and second-order formulations strictly requires a topological counterterm sourced by a bosonic chiral anomaly. Solving this deformed theory at large $N$ yields two primary results. First, we analytically determine the nonperturbative vacuum structure of the self-dual theory, a self-dual vacuum with a dynamically generated field-strength condensate. Second, we resolve a fundamental paradox where saddles with $(\theta + 2\pi n) \sim O(N)$ ($n$ is branch number) spuriously yield lower energy densities than the physical ground state. Because the effective action possesses an essential singularity at $F=0$, we show that the Lefschetz thimble analysis must be generalized to include boundary thimbles. A boundary Stokes phenomenon renders the problematic saddles topologically inactive, fully restoring the validity of the large-$N$ expansion for strongly coupled theories.

We report the first numerical examination of symmetric mass generation (SMG) for domain-wall fermions. Our simulation on a two-dimensional Euclidean lattice computes the path-integral of the Fidkowski-Kitaev Majorana chain with two boundaries, corresponding to the two (physical and mirror) walls. We demonstrate by evaluating the lattice Dirac operator eigenvalue spectrum that the local four-Fermi interaction selectively gaps the edge fermions on the mirror wall while leaving the physical wall intact. We further identify a characteristic signature of SMG in the path-integral: the gap of the Dirac operator opens along the imaginary axis of the complex spectrum, in contrast to the standard mass shift in the real direction. The conventional hybrid Monte Carlo algorithm remains practical with reweighting the complex phase of the Pfaffian, which is found to be remarkably small throughout the simulation. These results provide a practical nonperturbative framework for interaction-induced mirror-fermion decoupling of lattice domain-wall fermions.

We introduce latent geometry in BFSS/BMN models. Before an emergent geometry evaporates at the geometric transition, large-$d$ Gaussianization encodes its information in the exceptional $N=2$ sector selected by the baby fuzzy sphere, a single active spin-$1/2$ Pauli block. Dimensional reduction, finite-$N$ Gaussianization and exact Molien–Weyl projection transport this encoding to mass-deformed BFSS$_2$. At $N=2$, the same stable BFSS$_2$ oscillator admits inequivalent unitary $\mathbf{H}^2_\theta=\mathbf{EAdS}^2_\theta$ and $\mathbf{dS}^2_\theta$ decodings, realizing spacetime transmutation and the emergence of Lorentzian time.

We calculate the electromagnetic form factors of nucleons bound in finite nuclei and make predictions to the ratio between the electric ($G_E^*$) and magnetic ($G_M^*$) form factors in terms of the square of the four-momentum transfer $Q^2$. We extend our previous constant-density calculations within the covariant spectator-QMC framework by incorporating the spatial nuclear density profiles of finite nuclei and quantify the deviations from the average-density approximation used in our previous applications. The impact of the medium effects can then be observed considering the ratio between $G_E^*/G_M^*$ and the ratio in free space $G_E/G_M$, that define the proton electromagnetic double ratio associated with a given nucleus. The double ratio is expected to remove some systematic uncertainties. There is the expectation that ratios $G_E^*/G_M^*$ associated with the bound protons inside the nucleus will be measured in the near future in polarization-transfer experiments $(\vec{e} A, e'\! A' \vec{p})$. Anticipating future measurements on the subject, we make predictions for the double ratios, to be compared with the average measurements on the energy states of protons bound to nuclei. We consider the nuclei $^{12}$C, $^{16}$O and $^{40}$Ca. We conclude that the form factors calculated using nuclear density profile function $\rho(r)$ are less suppressed than in the case of the results calculated using the average nuclear density. The results indicate that the relative importance of the low-density surface region increases with $Q^2$, leading to a weaker suppression than that predicted by the average-density approximation. We also make predictions for the ratios associated with neutrons bound to nuclei.

Lattice systems with multiple nearby transitions pose two related challenges: resolving distinct transition scales and identifying the degrees of freedom primarily associated with each transition. We show that the intrinsic dimension of Monte Carlo configuration ensembles, estimated by the two-nearest-neighbors method, provides a geometric diagnostic for both problems. In the two-dimensional $q$-state clock model, the intrinsic dimension distinguishes the ordered, quasi-critical, and disordered regimes for both well-separated ($q=9$) and closely spaced ($q=5$) Berezinskii–Kosterlitz–Thouless transitions. In the $q=5$ case, the intermediate phase appears as a broad low-dimensional valley even when energy and magnetization do not separately resolve the two transitions. In the four-dimensional $U(1)$ Higgs model, we introduce channel-decomposed intrinsic dimensions based on gauge-invariant plaquette and Higgs variables. The dominant response of each channel tracks transitions associated with the corresponding degrees of freedom, while the combined channel retains features of both. We further show that intrinsic dimensions evaluated directly on gauge-variant fields are dominated by gauge-orbit directions, demonstrating the importance of removing gauge redundancy before interpreting configuration-space geometry. These results establish channel-decomposed intrinsic dimension as a geometric probe of lattice systems with multiple transitions and motivate its application to disentangling deconfinement and chiral crossover scales in full QCD.

Light-cone distribution amplitudes (LCDAs) are essential to precision phenomenological studies. They can be accessed from lattice QCD through the large-momentum effective theory (LaMET) via quasi-distribution amplitudes (quasi-DAs). Factorization of quasi-DAs receive power corrections in inverse powers of the hadron momentum, including target-mass and higher-twist corrections. In this work, we present the first systematic analysis of such power corrections for the leading-twist baryon quasi-DA. Establishing the moment relation between the quasi-DA and the LCDA, we derive an exact closed-form relation that resums target-mass correction to all orders at leading twist. This result also applies to heavy baryons and to quasi-transverse-momentum-dependent distributions. We numerically assess these corrections for the $\Lambda$ baryon quasi-DA using existing lattice data, finding that the target-mass correction decreases rapidly with increasing baryon momentum and is almost negligible in the endpoint regions. In addition, we explicitly construct the next-to-leading-twist operators entering the quasi-DA factorization. Our results are a first step toward quantifying the power corrections in future lattice determinations of light or heavy baryon LCDAs.

Quantum computers offer the potential to directly probe the dynamics of strongly coupled quantum field theories. As a step towards reaching this potential, local Krylov-based truncations of a pure SU(2) lattice gauge theory on a triangular lattice are constructed. Adjoint strings connected to dynamical gluons are constructed in this truncated theory, and the resonances dominating the long-term dynamics at a large value of the gauge coupling are determined. Local operators are constructed to identify string oscillations and breakings. This is used to perform a quantum simulation of adjoint string breaking on an $8\times8$ and $16\times8$-site lattice with ibm_boston using all 156 qubits. Quantitative agreement with tensor network simulations is obtained for circuits with 7,634 CZ gates with a two-qubit gate depth of 218. In this simulation, the rates of oscillations and glueball production are identified with a distinctly non-Abelian signature of the underlying gauge group.