Emergent Symmetries in Quantum Field Theory

Quantum field theories exhibit various interesting phenomena at strongly coupled fixed points of their renormalization group flows. One of these is a possible enhancement of the global symmetry of the UV model in the IR, and even though many examples of such enhancements are known, we still lack a general understanding of when they could happen and what is the general mechanism behind this phenomenon. In this lecture, we will focus on theories with supersymmetry which serve as simple toy models where the situation is more tractable, and discuss how theories with emergent symmetries can be obtained from dualities, models with special chiral ring relations or from the compactification of a higher dimensional theory. Going in the opposite direction, we will also show how emergent symmetries can be employed to find new dualities and compactifications of higher dimensional theories.