Gauge fields, membranes, and subdeterminant vector models.
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.
Leigh
Robert G
RG
Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA.
Mauri
Andrea
A
Minic
Djordje
D
Petkou
Anastasios C
AC