Gauge Fields, Membranes and Subdeterminant Vector Models

TL;DR

This paper introduces new classically marginal N-vector models in 3 and 4 dimensions with scalar potentials as subdeterminants, exploring their large-N behavior and connections to strings, membranes, and novel spin systems.

Contribution

It presents a novel class of models with subdeterminant scalar potentials, generalizing the BLG model and analyzing their effective potentials and large-N scaling.

Findings

Effective potentials show intriguing large-N scaling behaviors

Models relate to strings, membranes, and ternary spin systems

Scalar potentials expressed as subdeterminants of symmetric matrices

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 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.