16:00
I will review recent work on N=(2,2) boundary conditions of 3d
N=4 theories which mimic isolated massive vacua at infinity. Subsets of
local operators supported on these boundary conditions form lowest
weight Verma modules over the quantised bulk Higgs and Coulomb branch
chiral rings. The equivariant supersymmetric Casimir energy is shown to
encode the boundary ’t Hooft anomaly, and plays the role of lowest
weights in these modules. I will focus on a key observable associated to
these boundary conditions; the hemisphere partition function, and apply
them to the holomorphic factorisation of closed 3-manifold partition
functions and indices. This yields new “IR formulae” for partition
functions on closed 3-manifolds in terms of Verma characters. I will
also discuss ongoing work on connections to enumerative geometry, and
the construction of elliptic stable envelopes of Aganagic and Okounkov,
in particular their physical manifestation via mirror duality
interfaces.
This talk is based on 2010.09741 and ongoing work with Mathew Bullimore
and Samuel Crew.