Lattice QCD is a model-independent and mathematically rigorous first-principles approach to studying nonperturbative Quantum Chromodynamics (QCD) using a discrete spacetime lattice which can be simulated on a computer. Putting the quark fields on the sites of the lattice and the gauge fields on the links connecting neighbouring sites, the path integral for QCD can be written as a probability distribution over a very large space of configurations, which can be efficiently sampled using Monte-Carlo simulations. To fully control all systematic uncertainties, extrapolations to vanishing lattice spacing and infinite lattice volume are required.

Chiral Perturbation Theory is an effective field theory for the low-energy regime of QCD, which is based on the approximate chiral symmetry of QCD with light quarks and uses light pseudoscalar mesons (pions, kaons, …) as the relevant degrees of freedom. Further extensions can be made to incorporate baryons, vector mesons and heavy-quark mesons. Chiral Perturbation Theory is important, among other things, to make the connection between lattice simulations at unphysical quark masses and the real world.

The locality and causality of Green functions in Quantum Field Theory enables a description of their analytic structure in terms of integrals along cuts in the complex plane. This general idea gives rise to tools such as the Källén-Lehmann spectral representation, the optical theorem and sum rules, which can be used to derive rigorous bounds on various quantities in terms of experimentally observable cross sections.

Few-body methods are essential tools for the study of light nuclei, where the number of nucleons is small enough to allow for exact or near-exact solutions of the Schrödinger equation using realistic two- and three-nucleon interactions. Approaches such as the hyperspherical harmonics method enable accurate predictions of bound states, scattering observables, and response functions. By leveraging these techniques, we gain deep insight into the structure and dynamics of light nuclei, while also testing and constraining nuclear forces.

Many-body methods such as coupled-cluster (CC) theory are powerful and systematically improvable ab initio approaches for describing the structure of medium-mass nuclei, typically ranging from oxygen to tin. CC theory has been successfully adapted to nuclear physics due to its ability to capture a significant portion of many-body correlations while maintaining computational tractability. It is particularly effective for closed-shell nuclei and their neighbours, and has been extended to include three-nucleon forces and continuum effects, enabling precise predictions of binding energies, excitation spectra, radii, and, more recently, electroweak reactions.

Effective field theories (EFTs) offer a systematic approach to describing nuclear interactions at low energies by exploiting a separation of scales. In nuclear physics, chiral EFT is widely used to derive two- and many-body forces, as well as electroweak currents, in a way that is consistent with the symmetries of QCD, particularly chiral symmetry. Complementing this, halo EFT is a specialized framework tailored to describe weakly bound systems—such as halo nuclei—where a clear separation exists between the core and valence nucleons. It is particularly powerful in reaction theory, making it a valuable tool for interpreting experiments near the drip lines.