title: Gauge fields, membranes, and subdeterminant vector models.
abstract: 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 can be thought of as a generalization of the scalar sector of the Bagger-Lambert-Gustavsson model. Using the Hubbard-Stratonovich transformation we calculate their effective potentials which exhibit intriguing large-N scaling behaviors. We comment on the possible relevance of our models to strings, membranes, and also to a class of novel spin systems that are based on ternary commutation relations.
authors.affiliation: Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA.
authors.forename: Robert G
authors.initials: RG
authors.lastname: Leigh
authors.forename: Andrea
authors.initials: A
authors.lastname: Mauri
authors.forename: Djordje
authors.initials: D
authors.lastname: Minic
authors.forename: Anastasios C
authors.initials: AC
authors.lastname: Petkou