Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra Models

TL;DR

This paper explores the relationships between reduced Chern-Simons quiver theories, 3-algebra models, and matrix models, revealing new twists and localization techniques to compute BPS spectra and moduli spaces in supersymmetric theories.

Contribution

It introduces explicit mappings between Chern-Simons quiver matrix models and dual IKKT models, and constructs a new topological twist of the IKKT model.

Findings

Derived explicit maps between matrix models

Constructed a new topological twist of the IKKT model

Localized the partition function onto a moduli space related to 3-algebra relations

Abstract

We study the BPS spectrum and vacuum moduli spaces in dimensional reductions of Chern-Simons-matter theories with N>=2 supersymmetry to zero dimensions. Our main example is a matrix model version of the ABJM theory which we relate explicitly to certain reduced 3-algebra models. We find the explicit maps from Chern-Simons quiver matrix models to dual IKKT matrix models. We address the problem of topologically twisting the ABJM matrix model, and along the way construct a new twist of the IKKT model. We construct a cohomological matrix model whose partition function localizes onto a moduli space specified by 3-algebra relations which live in the double of the conifold quiver. It computes an equivariant index enumerating framed BPS states with specified R-charges which can be expressed as a combinatorial sum over certain filtered pyramid partitions.