Physics of Quarks and Gluons and Their Vacuum Structure

The fundamental constituents of matter — protons and neutrons — are composed of quarks and gluons, whose physics is described by quantum chromodynamics (QCD), a quantum field theory. Theoretical understanding of QCD still harbors many fundamental mysteries, typified by quark confinement: why quarks are never observed individually, appearing only inside protons, neutrons, and the like. This talk first touches on the difficulty and fascination of understanding the low-energy physics and vacuum structure of QCD, and then introduces recent work on semiclassical analysis of the QCD vacuum via T² compactification.