We consider the Polyakov loop correlator in the confining phase of large $N$ Yang-Mills theory in three and four dimensions. It can be computed by summing over the exchange of closed flux tubes winding around the thermal cycle. At short separations, the leading divergence is controlled by perturbation theory. Combining these two facts allows us to determine the asymptotic spectral density of string states contributing to the correlator. This sharply relates the weakly-coupled UV of the gauge theory to the dynamics of highly energetic flux tubes. Then, in a toy integrable setting, we explore how this can bound the scattering data of the Goldstone modes on top of a long string. We derive a bound on the asymptotic behavior of the reflection amplitude of Goldstones against the flux tube boundary sourced by the Polyakov line, and rule out an asymptotically linear phase shift for the S-matrix. Along the way, we discuss how causality can impose bounds on thermodynamic quantities, and show how the positivity of time delays follows from unitarity and analyticity of $2d$ massless elastic S-matrices. We include a review on reflection amplitudes, and their computation in the theory of long effective strings.

We study the effects of uncorrelated quenched disorder to the phase diagram and continuous transitions of three-dimensional lattice ${\mathbb Z}_2$ gauge Higgs models. For this purpose, we consider two types of quenched disorder, associated with the sites and plaquettes of the cubic lattice. In both cases, for sufficiently weak disorder, the phase diagram remains similar to that of the pure system, showing two different phases (one of them being a topologically ordered phase), separated by two different continuous transition lines. However, the quenched disorder changes the universality classes of the critical behaviors along some of the transition lines. The random-plaquette disorder turns out to be relevant along the topological ${\mathbb Z}_2$ gauge transition line, so the critical behaviors belong to the different random-plaquette $\mathbb{Z}_2$ gauge (RP${\mathbb Z}_2$G) universality class with length-scale exponent $\nu=\nu_{\rm rp}\approx 0.82$; on the other hand, it turns out to be irrelevant along the other Ising$^\times$ transition line (a variant of the Ising transitions with a gauge-dependent order parameter), leaving unchanged its asymptotic critical behaviors with $\nu=\nu_{\cal I}\approx 0.63$. The random-site disorder leads to a substantially different scenario: it destabilizes the Ising$^\times$ critical behaviors of the pure model, changing them into those of the randomly-dilute Ising$^{\times}$ (RDI$^{\times}$) universality class with $\nu=\nu_{\rm rdi}\approx 0.68$, while the critical behaviors along the other ${\mathbb Z}_2$ gauge topological transition line remains stable, with $\nu=\nu_{\cal I}\approx 0.63$.

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. In order to address discrepancies in the literature, the calculation is performed at a heavy pion mass in the limit that the light quark masses are equal to the physical strange quark mass, $m_\pi = m_K \simeq 714 $ MeV. Using a state-of-the-art momentum space method, we rule out the presence of a bound di-nucleon in both the isospin 0 (deuteron) and 1 (di-neutron) channels, in contrast with many previous results that made use of compact hexaquark creation operators. In order to diagnose the discrepancy, we add such hexaquark interpolating operators to our basis and find that they do not affect the determination of the two-nucleon finite volume spectrum, and thus they do not couple to deeply bound di-nucleons that are missed by the momentum-space operators. Further, we perform a high-statistics calculation of the HAL QCD potential on the same gauge ensembles and find qualitative agreement with our main results. We conclude that di-nucleons do not form bound states at heavy pion masses and that previous identification of deeply bound di-nucleons must have arisen from a misidentification of the spectrum from off-diagonal elements of a correlation function.

We propose a new method to investigate the existence and location of the conjectured high-temperature critical point of strongly interacting matter via contours of constant entropy density. By approximating these lines as a power series in the baryon chemical potential $\mu_B$, one can extrapolate them from first-principle results at zero net-baryon density, and use them to locate the QCD critical point, including the associated first-order and spinodal lines. As a proof of principle, we employ currently available continuum-extrapolated first-principle results from the Wuppertal--Budapest collaboration to find a critical point at a temperature and a baryon chemical potential of $T_c = 114.3 \pm 6.9$ MeV and $\mu_{B,c} = 602.1 \pm 62.1$ MeV, respectively. We advocate for a more precise determination of the required expansion coefficients via lattice QCD simulations as a means of pinpointing the location of the critical endpoint in the phase diagram of strongly interacting matter.

This review has explored the fundamental principles of thermal field theory in the context of a background magnetic field, highlighting its theoretical framework and some of its applications to the thermo-magnetic QCD plasma generated in heavy-ion collisions. Our discussion has been limited to equilibrium systems for clarity and conciseness. We analysed bulk thermodynamic characteristics, including the phase diagram as well as real-time observables, shedding light on the behaviour and dynamics of the thermo-magnetic QCD medium relevant to heavy-ion physics.

Hadronic $\tau$ decays present an opportunity to determine the isovector part of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon in a way complementary to $e^+e^-\to\text{hadrons}$ cross sections. However, the required isospin rotation is only exact in the isospin limit, and corrections need to be under control to draw robust conclusions, most notably for $\tau\to\pi\pi\nu_\tau$ decays to determine the two-pion contribution, $a_\mu^\text{HVP, LO}[\pi\pi,\tau]$. In this work, we present a novel analysis of the required radiative corrections using dispersion relations, thereby extending in a model-independent way the previous analysis in chiral perturbation theory (ChPT) beyond the threshold region. In particular, we include the dominant structure-dependent virtual corrections from pion-pole diagrams, leading to sizable changes in the vicinity of the $\rho(770)$ resonance. Moreover, we work out the matching to ChPT and devise a strategy for a stable numerical evaluation of real-emission contributions near the two-pion threshold, which proves important to capture isospin-breaking corrections enhanced by the threshold singularity. For the numerical analysis, we use a dispersive representation of the pion form factor including the $\rho'$, $\rho''$ resonances, perform fits to the available data sets for the $\tau\to\pi\pi\nu_\tau$ spectral function, and calculate the corresponding radiative correction factor $G_\text{EM}(s)$ in a self-consistent manner. Based on these results, we evaluate the $\tau$-specific isospin-breaking corrections to $a_\mu^\text{HVP, LO}[\pi\pi,\tau]$.

We propose and analyze a trapped-ion quantum simulator of the Jackiw-Rebbi model, a paradigmatic quantum field theory in (1+1) dimensions where solitonic excitations of a scalar field can bind fermionic zero modes leading to fractionally-charged excitations. In our approach, the scalar field is a coarse-grained description of the planar zigzag ion displacements in the vicinity of a structural phase transition. The internal electronic states of the ions encode spins with interactions mediated by the transverse phonons and in-plane spin-phonon couplings with a zigzag pattern, which together correspond to a Yukawa-coupled Dirac field. Instead of assuming a fixed soliton background, we study the effect of back-reaction and quantum fluctuations on the coupled dynamics of the full fermion-boson system. We start by applying a Born-Oppenheimer approximation to obtain an effective Peierls-Nabarro potential for the topological kink, unveiling how the fermionic back-reaction can lead to localization of the kink. Beyond this limit, a truncated Wigner approximation combined with fermionic Gaussian states captures the quantum spreading and localization of a kink and kink-antikink scattering. Our results reveal how back-reaction and quantum fluctuations modify the stability and real-time evolution of fractionalized fermions, predicting experimentally accessible signatures in current trapped-ion architectures.