Integrability methods in quantum field theory

An integrable quantum field theory is a special type of quantum field theory possessing infinitely many local conserved currents, which can generally only be defined in 1+1-dimensional spacetime. Such quantum field theories can be solved exactly using integrability methods and serve as an important prototype for studying non-perturbative quantum field theory. In recent years, integrability methods have been applied to solve certain quantum field theories in higher dimensional spacetimes, playing an increasingly significant role in deepening our understanding of higher-dimensional quantum field theories and quantum gravity. This article introduces the concept of integrable quantum field theories and the main ideas behind their exact solutions.