Super-Galilei Invariant Field Theories in 2+1 Dimensions

TL;DR

This paper develops an extended super-Galilei invariant field theory in 2+1 dimensions, exploring its algebraic structure, interactions, and implications for superstring theory, highlighting increased restrictions due to supersymmetry.

Contribution

It introduces a gradation extension of the Galilei group, constructs related field theories, and analyzes their relevance to superstring theory with matrix fields.

Findings

Non-relativistic Super-Chern-Simons theory is a special case.

Matrix-valued fields are highly constrained by supersymmetry.

The extended algebra provides new insights into non-relativistic supersymmetric models.

Abstract

We extend the Galilei group of space-time transformations by gradation, construct interacting field-theoretic representations of this algebra, and show that non-relativistic Super-Chern-Simons theory is a special case. We also study the generalization to matrix valued fields, which are relevant to the formulation of superstring theory as a $1/N_c$ expansion of a field theory. We find that in the matrix case, the field theory is much more restricted by the supersymmetry.