We calculate the spatial string tension in 2+1 flavour QCD in $(3{+}1)$ dimensions within a temperature range of $[166\,\mathrm{MeV},\,1000\,\mathrm{MeV}]$ using spatial Wilson loops with HYP smearing. We use the Highly Improved Staggered Quark action for fermions and the tree-level Symanzik improved gauge action for gluons at two lattice spacings corresponding to temporal extents $N_\tau = 8$ and $10$. We then compare our results with dimensionally reduced effective theories at high temperatures (EQCD and MQCD) to test the onset of dimensional reduction in QCD.

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

Coulomb-gauge quasi-parton distributions can be computed directly in momentum space on a finite lattice, enabled by the commutativity of their renormalization and Fourier transform. This approach removes the formal inverse problem in coordinate-space methods. Our momentum-space pion quasi-distributions agree with coordinate-space results Fourier transformed with asymptotic extrapolation, indicating that the formal inverse problem in the latter is not a concern at this volume. We further extend the framework to higher dimensions and obtain the first 3D image of the pion directly from lattice QCD.

One of the goals of quantum simulation is to provide novel insights into quantum systems, such as the gauge theories that are relevant for high-energy and nuclear physics. Recent years have seen rapid improvements in both the hardware and software necessary for these simulations. A central consideration in the design of such simulations is the quantum complexity of a given quantum state. This work takes a step towards studying a specific kind of complexity, namely the non-stabilizerness, in a simple yet non-trivial system: SU(2) lattice gauge theory of two plaquettes. The non-stabilizerness of low-energy eigenstates is studied and the implications for quantum simulations are discussed. The real-time evolution of this system is simulated on ibm_marrakesh and the non-stabilizerness is measured using a random measurement protocol. New techniques enhancing the efficiency of this protocol are developed, including both a new way to calculate the estimator for non-stabilizerness and a flexible error mitigation technique called Bit String Decoherence Renormalization. This mitigation method is central to accurately resolving the experimental time dependence of non-stabilizerness, and is anticipated to have broad applicability in digital quantum simulations.

The standard approach to perturbation theory for finite-temperature quantum field theories has several issues, including the appearance of ill-defined on-shell contributions in the real-time formulation, and infrared diverges in massless theories. Earlier studies indicate that these issues all stem from the inconsistent thermal generalisation of the Gell-Mann-Low relation, which forms the foundation of perturbation theory in vacuum. This inconsistency arises from the use of free scattering states in the relation, which are known not to exist in interacting thermal theories. In this work, we propose a generalisation of the Gell-Mann-Low relation for scalar theories based on non-perturbative spectral insights, namely that finite-temperature scattering states can be described by damped but stable particle-like excitations, so-called thermoparticles. The perturbative expansion of this generalised relation gives rise to contributions with exactly the same topology as the standard finite-temperature approach, except that now the propagators appearing in this expansion are not those of a free field but of thermoparticles, which depend on the dynamics of the theory. We demonstrate that thermoparticle perturbation theory resolves the known problems of the standard approach. Furthermore, by comparing imaginary-time calculations at two-loop level with numerical lattice simulations of two-point correlation functions in massive $\phi^{4}$ theory, we explicitly show that this framework gives rise to precise predictions, as in the vacuum case, in stark contrast to the standard approach.

Some cumulants of the fluctuations of conserved charges soon above the chiral crossover behave as if the quarks were free. This was taken by many as evidence of deconfinement. At the same temperatures the mesonic correlators reveal the chiral spin and SU(4) symmetries, indicating that the propagating degrees of freedom are massless quarks connected into color singlets by the chromoelectric confining string. These correlators are qualitatively different from the free quark gas. Here we clarify the reason for the difference. The conserved quark number densities do not propagate in time but do propagate in spatial directions. The mesonic propagators calculated in full QCD differ radically from the free quark loop (quark gas) above T_ch. In contrast, the quark number density spatial propagator in full QCD at T > 220 MeV is very close to the free quark loop. In other words, the conserved charges do not see confinement, in contrast to the mesonic correlators. This is consistent with the well understood quark-hadron duality at T=0 in e^+e^- -> hadrons, where at invariant masses above 2 GeV the cross-section in the confining regime is represented by the free quark loop plus small perturbative corrections. All these features above T_ch but below the deconfinement temperature T_d can be combined within the following microscopic picture of the stringy fluid matter. It is a medium of the overlapping strongly interacting color singlet clusters. The quark interchanges between the clusters, required by Paili principle, make the quarks quasifree, which is reflected in fluctuations of conserved charges.

We present the first direct calculation of the tensor transition form factors (TFFs) of the $N \to \Delta$ transition using the QCD light-cone sum rules. The matrix element of the tensor current sandwiched between the nucleon and $\Delta$ states is parametrized in terms of four independent form factors, derived from Lorentz covariance, Hermiticity, parity, time-reversal, and the Rarita--Schwinger constraints. The natural-parity character of the $1/2^+ \to 3/2^+$ channel combined with the spin-$1$ polarization content of the Rarita--Schwinger spinor imposes a trailing $\gamma_5$ in the parametrization, in analogy with the gravitational $N \to \Delta$ case. Using the nucleon distribution amplitudes expanded in wavefunctions of different twists, we compute the four TFFs in the spacelike range $1 \leq Q^2 \leq 10$~GeV$^2$ for two sets of light-cone input parameters, and extrapolate to the static limit through multipole fit functions. A flavor decomposition into $u$- and $d$-quark contributions reveals three qualitatively distinct patterns among the four TFFs: $d$-quark dominance with $|F^d| \gg |F^u|$ for $F_1$ and $F_2$ -- in marked contrast to the diagonal nucleon tensor charges where the $u$-quark dominates; an antisymmetric flavor structure $F^u \approx -F^d$ for $F_3$, which naturally explains the absence of a stable isoscalar sum rule for this form factor; and comparable but opposite-sign flavor contributions to $F_4$, with a suppressed isoscalar combination. The TFFs provide chiral-odd information complementary to the electromagnetic and gravitational $N \to \Delta$ transitions and offer model-independent input for future analyses of transversity-related transition observables, to be checked against lattice QCD and other phenomenological approaches.

QCD-like theories with $N_F=2$ fermion flavours in real and pseudoreal representations are studied within Chiral Perturbation Theory. For the pseudoreal symmetry-breaking pattern $SU(4)/Sp(4)$, the reduced NLO Lagrangian is derived. The NLO and NNLO corrections to the pion masses, decay constants, and vacuum condensates are calculated for non-degenerate fermion masses, extending previous results obtained for degenerate masses and for the non-degenerate case at NLO. Using the available spectroscopic and scattering lattice data for the $Sp(N_c=4)$ gauge theory with two fermion flavours, fits of the NLO low-energy constants are performed at NNLO precision. It is found that higher-order corrections are important for reproducing lattice observables and have a significant impact on the phenomenology of strongly interacting pionic dark matter, particularly in the regime of big $M_\pi/F_\pi$.

The hadronic tensor encodes crucial information regarding the internal structure of hadrons, reflecting the non-perturbative features of quantum chromodynamics (QCD). In this work, we directly compute the hadronic tensor within (1+1)-dimensional $\rm U(1)$ and $\rm SU(2)$ gauge theories by evaluating real-time current-current correlation functions. Utilizing quantum algorithms executed on classical hardware, we demonstrate that the hadron form factors for both meson and baryon states can be reliably extracted from the hadronic tensor. Our methodology is validated by strong agreement with both direct calculation and exact diagonalization of the form factors.

We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers: constant-depth circuits of local unitaries that transform not-on-site symmetries into on-site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice rotor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for $U(1)$ symmetries with mixed 't Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional "3450" chiral gauge theory, and we argue that a related construction applies to the $U(1)$ hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories.