Understanding gauge theories such as QCD (the fundamental theory of interactions between quarks and gluons) is one of the most important problems in theoretical physics since it presents
perhaps the deepest challenge for non-perturbative physics that cannot be captured via conventional Feynman diagrams. Gauge theories emerge even in many strongly-correlated electronic
systems due to lattice constraints. In gauge theories such as QCD, the force between the elementary quarks and gluons grow with mutual distance due to quantum fluctuations leading to
confinement -- the bizarre feature that quarks and gluons cannot be isolated from their bound states eg protons, neutrons, pions and glueballs. Understanding the mechanism of confinement
going beyond perturbative processes remains elusive since its Nobel-prize winning discovery.
N=2 SUSY gauge theories owing to their supersymmetry are more amenable for theoretical understanding. One major success has come due to the works of Seiberg and Witten which showed that one can use supersymmetry and non-perturbative dualities (in which the same physical system can have different dual descriptions in terms of elementary degrees of freedom) to construct the leading order low energy dynamics *exactly*. Furthermore, they showed that a proposed mechanism of confinement called monopole condensation is explicitly realised after suitable deformations (which break supersymmetry partially). Since the works of Seiberg and Witten, a lot of progress has been made in this field particularly in relation to the understanding of dualities which have led to explicit examples of a class of field theories not amenable to conventional Lagrangian descriptions and which have allowed us to compute a lot of physical observables exactly and explicitly. These developments have enriched our understanding of gauge theories.
The second part of Prof Sujay Ashoke's lectures will explore how embeddings in string theory can help us to find easily the low energy effective actions of a large class of N=2 supersymmetric gauge theories exactly.