Effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of Quantum Chromodynamics. We review the foundations of this approach and discuss its application for light nuclei at various resolution scales. The extension of this approach to many-body systems is briefly sketched. Commissioned article for Reviews of Modern Physics Contents I. QCD and Nuclear Forces 1 A. Chiral symmetry 2 B. Scales in nuclear physics 3 C. Conventional approaches to the nuclear force problem 4 D. Brief introduction to effective field theory 5 E. First results from lattice QCD 6 F. Observables and not-so observable quantities 8 II. EFT for Few-Nucleon Systems: Foundations and Applications 8 A. EFT with contact interactions and universal aspects 8 B. Chiral EFT for few nucleons: foundations 12 C. Chiral EFT for few nucleons: applications 21 D. The role of the ∆-isobar 25 E. Few-nucleon reactions involving pions 30 F. Hyperon-nucleon & hyperon-hyperon interactions 31 G. Nuclear lattice simulations 33 H. Quark mass dependence of nuclear forces and IR limit cycle in QCD 36 III. Towards a Many-Body EFT for Nuclei 39 A. In-medium chiral perturbation theory 39 B. Perturbative chiral nuclear dynamics 41 C. EFT for halo nuclei 42 D. V low k potentials: construction and applications 43 E. Lattice simulations of many-nucleon systems 44

ABSTRACT:We review the implications of the spontaneous chiral symmetry breaking in QCD for processes involving one, two or more nucleons.

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We consider the two-nucleon system at next-to-next-to-next-to-leading order (N^3LO) in chiral effective field theory. The two-nucleon potential at N^3LO consists of one-, two- and three-pion exchanges and a set of contact interactions with zero, two and four derivatives. In addition, one has to take into account various isospin-breaking and relativistic corrections. We employ spectral function regularization for the multi-pion exchanges. Within this framework, it is shown that the three-pion exchange contribution is negligibly small. The low-energy constants (LECs) related to pion-nucleon vertices are taken consistently from studies of pion-nucleon scattering in chiral perturbation theory. The total of 26 four-nucleon LECs has been determined by a combined fit to some np and pp phase shifts from the Nijmegen analysis together with the nn scattering length. The description of nucleon-nucleon scattering and the deuteron observables at N^3LO is improved compared to the one at NLO and NNLO. The theoretical uncertainties in observables are estimated based on the variation of the cut-offs in the spectral function representation of the potential and in the regulator utilized in the Lippmann-Schwinger equation.Comment: 62 pp, 13 fig