Membrane matrix models and 3-algebras
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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.