Piljin Yi, KIAS
Title: Witten Index, Wall-Crossing, and Threshold Bound States
Abstract: D-brane bound state problems in general and wall-crossing problems in particular can be addressed explicitly via Witten index computation of d=1 GLSM's. When the low energy dynamics of the latter involves gapless asymptotic flat directions, the bound state, if any, would be at threshold and many subtleties emerge in trying to count them.
In this talk, we revisit the supersymmetric localization method for twisted partition functions of such theories, and discuss how the latter tends to produce misleading answers and also how, sometimes, the true Witten index can nevertheless be salvaged from such computations. We close by pointing out that the notion of the rational invariant, as in Kontsevich-Soibelman's wall-crossing algebra, is a manifestation of such subtleties for U(N) groups, and offering a generalization to all Lie Groups.
