Membrane matrix models and 3-algebras
Abstract
In this thesis we study the BPS spectrum and vacuum moduli spaces of membrane
matrix models derived from dimensional reduction of the BLG and ABJM M2-
brane theories. We explain how these reduced models may be mapped into each
other, and describe their relationship with the IKKT matrix model. We construct
BPS solutions to the reduced BLG model, and interpret them as quantized Nambu-
Poisson manifolds. We study the problem of topologically twisting the reduced
ABJM model, and along the way construct a new twist of the IKKT matrix model.
We construct a cohomological matrix model whose partition function localizes onto
the BPS moduli space of the ABJM matrix model. This partition function computes
an equivariant index enumerating framed BPS states with specified R-charges.