We investigate the multipole structure of the nucleon tensor form factors within the chiral quark-soliton model based on the $1/N_c$ expansion. Extending the previous leading-order analysis~\cite{Ghim:2025gqo}, we include the rotational $1/N_c$ corrections. These corrections provide the leading nonvanishing contributions to the flavor components that are absent at leading order, thereby completing the flavor decomposition of the tensor multipole form factors at the present order. We numerically evaluate the isoscalar tensor charge, the isovector anomalous tensor magnetic moment, and the isoscalar tensor quadrupole moment, obtaining $g_T^{u+d}=0.81$, $\kappa_T^{u-d}=1.97$, and $E_T^{u+d}(0)=5.98$, respectively. The isoscalar tensor charge and quadrupole moment are mainly governed by the valence-quark contribution, whereas the isovector anomalous tensor magnetic moment receives a sizable Dirac-sea contribution. We also examine the momentum-transfer dependence of the corresponding form factors. They decrease monotonically with increasing $-t$. In particular, the isovector anomalous tensor magnetic form factor shows a pronounced falloff in the small-$|t|$ region, reflecting the importance of the Dirac sea in the tensor dipole structure.

We study the \(N=2\), large--\(d\) sector of BFSS/BMN-type matrix quantum mechanics on the lattice in the Gaussian regime. We develop a radial endpoint formulation in which the bulk, gauge, and longitudinal degrees of freedom are integrated out, leaving transverse endpoint variables governed by an effective holonomy potential. We show that this planar endpoint formulation is equivalent to the angular Molien--Weyl description of the gauge-projected partition function, up to a universal spectator factor. This relation allows the low-temperature expansion of the endpoint partition function to be obtained from the Molien--Weyl result, whose quadratic coefficient \(d(d+1)/2\) counts Gaussian singlet states above the vacuum. We then analyze the continuum limit of the quadratic coefficient and show that it separates into a Gaussian contribution, a \(D\)-channel, and a \(\beta\)-channel. The naive Gaussian term becomes trivial, while the exact holonomy kernel generates finite continuum contributions through singular dependence on the endpoint Gaussian width and anisotropic coupling. We then study the geometry of the holonomy potential and show that its relevant saddle is a constrained boundary saddle on the aligned branch, rather than an unconstrained critical point. The associated transverse expansion captures the local saddle geometry, but any finite polynomial truncation has a trivial continuum limit. Finally, we introduce a non-polynomial toy model based on \(V_{\rm toy}(B)=-\log\cosh B\), which provides a completion of the transverse expansion and reproduces exactly the continuum \(D\)-channel contribution \(-2d\). This prepares the geometric interpretation of the \(D\)-channel as a Wishart--Stiefel entropy associated with an emergent four-dimensional geometry embedded \(\mathbb R^d\) in the endpoint formulation.

We investigate the electromagnetic form factors of the nucleon within an effective chiral theory derived from the QCD instanton vacuum, taking into account the finite current quark mass. The momentum-dependent dynamical quark mass, generated by the instanton-antiinstanton medium, naturally plays the role of a regulator, so that no additional regularization is required to tame the divergences arising from quark loops. The instanton parameters, the average instanton size $\bar{\rho}=0.35$ fm and the average interdistance $\bar{R}=0.86$ fm, together with the dynamical quark mass at zero virtuality $M_0=385$ MeV, are all fixed by the saddle-point equation beyond the chiral limit, leaving no adjustable free parameter in the present calculation. We compute the Sachs electric and magnetic form factors of the proton and neutron, the nucleon charge and magnetization radii, the magnetic moments, and the ratios $\mu_{p,n} G_E^{p,n}(Q^2)/G_M^{p,n}(Q^2)$. The present results are compared with the experimental data, the chiral quark-soliton model ($\chi$QSM), and the Kelly parametrization. The proton charge radius, $\sqrt{\langle r^2 \rangle_\mathrm{ch}^p}=0.841$ fm, is in remarkable agreement with the recent muonic-hydrogen value, and the $Q^2$ dependence of the proton form-factor ratio $\mu_p G_E^p/G_M^p$ is reproduced very well, in clear contrast to the $\chi$QSM. The overall agreement with the experimental data confirms that the effective chiral theory derived from the QCD instanton vacuum provides a consistent and predictive framework for describing the electromagnetic structure of the nucleon.

Using numerical data coming from Monte Carlo simulations of four-dimensional Causal Dynamical Triangulations, we study how automated machine learning algorithms can be used to recognize transitions between different phases of quantum geometries observed in lattice quantum gravity. We tested seven supervised and seven unsupervised machine learning models and found that most of them were very successful in that task, even outperforming standard methods based on order parameters.

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.