Counting vacua in supersymmetric Yang-Mills theory
Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation
The recent progress concerning the Witten index in N=1 supersymmetric Yang-Mills theory is reviewed. Since 1982 there has been a controversy in counting vacua. The original calculation of the Witten index conflicted with expectations based on the chiral symmetry breaking picture. The controversy was resolved by Witten in 1998 who discovered additional disconnected components in the space of classical vacua in Yang-Mills theory compactified on a three-dimensional torus. We review the resolution of the controversy, describe those additional vacua and the corresponding gauge fields. We also discuss how the Witten index feels the physics of confinement and chiral symmetry breaking.