Regular Seminar Piljin Yi (KIAS)
This talk will explore topological invariants of susy gauge theories, with some emphasis on index-like quantities and the notion of holonomy saddles. We start with 1d refined Witten index computations where the twisted partition functions typically show rational, rather than integral, behavior. We will explain how this oddity is a blessing in disguise and propose a universal tool for extracting the truely enumerative Witten indices. In part, this finally put to the rest a two-decade-old bound state problems which had originated from the M-theory hypothesis. Along the way, we resolve an old and critical conflict between Kac+Smilga and Staudacher/Pestun, circa 1999~2002, whereby the notion of holonomy saddles emerges and plays a crucial role. More importantly, the holonomy saddle prove to be universal features of supersymmetric gauge theories when the spacetime include a small circle. We explore them further for d=4, N=1 theories, with much ramifications on recent claims on Cardy exponents of their partition functions.