Probing the Space of Toric Quiver Theories

TL;DR

This paper introduces a practical algorithm for generating and classifying toric Calabi-Yau quiver theories, enabling systematic exploration of their structure for D3 and M2 brane physics.

Contribution

It presents a new analytic approach and an efficient polynomial-time algorithm for classifying toric quiver theories with applications to string theory.

Findings

Developed a polynomial complexity algorithm for quiver classification

Classified quiver diagrams and superpotentials for small cases

Provided preliminary statistical analysis of the quiver theory space

Abstract

We demonstrate a practical and efficient method for generating toric Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume physics. A new analytic method is presented at low order parametres and an algorithm for the general case is developed which has polynomial complexity in the number of edges in the quiver. Using this algorithm, carefully implemented, we classify the quiver diagram and assign possible superpotentials for various small values of the number of edges and nodes. We examine some preliminary statistics on this space of toric quiver theories.