Coulomb branches of 3d N=4 gauge theories and motivic DT-invariants
Hiraku Nakajima (Research Institute for Mathematical Sciences)
MSRI: Simons Auditorium
Cremonesi, Hanany and others recently compute Coulomb branch Hilbert series of 3-dimensional N=4 gauge theories, and write down explicit combinatorial expressions. I identify their expressions with certain motivic DT-type invariants, defined by moduli stack of bundles over the projective line together with their sections. In particular, characters of coordinate rings of many hyper-Kaehler manifolds (such as instanton moduli spaces on R^4) are conjecturally equal to those invariants.