Gauge Fields, Membranes and Subdeterminant Vector Models

Understand

We present a class of classically marginal N-vector models in d=4 and d=3, whose scalar potentials can be written as subdeterminants of symmetric matrices.

• The d=3 case is a generalization of the scalar Bagger-Lambert-Gustavsson (BLG) model.
• Using the Hubbard-Stratonovich transformation we calculate their effective potentials which exhibit intriguing large-N scaling behaviors.
• We comment on the relevance of our models to strings, membranes and also to a class of novel spin systems that are based on ternary commutation relations.