Effective d=2 supersymmetric Lagrangians from d=1 supermatrix models

TL;DR

This paper derives a $d=2$ supersymmetric effective field theory from $d=1$, ${ m extstyle extbf{N}=2}$ supersymmetric matrix models, revealing insights into superstring dynamics and supersymmetry breaking via instantons.

Contribution

It constructs a $d=2$ supersymmetric effective field theory from $d=1$ supermatrix models, incorporating new fields and analyzing instanton solutions.

Findings

The effective theory is Poincare invariant.

Instanton solutions are identified and analyzed.

The theory encodes perturbative and non-perturbative superstring information.

Abstract

We discuss $d=1, {\cal N}=2$ supersymmetric matrix models and exhibit the associated $d=2$ collective field theory in the limit of dense eigenvalues. From this theory we construct, by the addition of several new fields, a $d=2$ supersymmetric effective field theory, which reduces to the collective field theory when the new fields are replaced with their vacuum expectation values. This effective theory is Poincare invariant and contains perturbative and non-perturbative information about the associated superstrings. We exhibit instanton solutions corresponding to the motion of single eigenvalues and discuss their possible role in supersymmetry breaking.