Supersymmetric Yang-Mills quantum mechanics: from two to ten space-time dimensions

by Jacek Wosiek (Max-Planck Inst. Munich & Jagellonian University, Cracow)

Thursday 30 Sept 2004, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

The last year's progress in solving the dynamics of the above systems will be discussed. In the D = 4, SU(2) model the precise spectrum is now available in all angular momentum channels. Localized and non-localized eigenstates coexist as required by supersymmetric interactions with flat valleys. All states are classified into easily identifiable supermultiplets, which in turn reveal some accidental degeneracy. The Witten index approaches the time-independent value of 1/4 also known from other calculations. In D = 10, contrary to lower dimensions, non-conservation of the Majorana-Weyl fermion number implies the complicated structure of the SO(9) representations in the Fock space. We present the explicit construction of the singlet state, which is vastly different from the usual empty state. This state provides the root for the subsequent construction of the basis.