Virginia TechLeigh, R. G.Mauri, A.Minic, DjordjePetkou, A. C.2013-12-102013-12-102010-06-01Leigh, Robert G. ; Mauri, Andrea ; Minic, Djordje ; et al., Jun 1, 2010. “Gauge Fields, Membranes, and Subdeterminant Vector Models,” PHYSICAL REVIEW LETTERS 104(22): 221801. DOI: 10.1103/PhysRevLett.104.2218010031-9007http://hdl.handle.net/10919/24501We 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.application/pdfenIn Copyrightm2 branesd3-branesPhysicsArticle - Refereedhttp://link.aps.org/doi/10.1103/PhysRevLett.104.221801https://doi.org/10.1103/PhysRevLett.104.221801