Multicritical Matrix-Vector Models of Quantum Orbifold Geometry

TL;DR

This paper develops matrix-vector models for quantum orbifold geometries, analyzing their amplitudes at multicritical points and comparing them to traditional matrix models, revealing both similarities and differences.

Contribution

It introduces new bosonic and fermionic matrix-vector models for orbifold string worldsheets and evaluates their amplitudes at multicritical points.

Findings

Some amplitudes resemble those of Hermitian matrix models

Other amplitudes differ significantly from Hermitian models

Derived explicit expressions for multiloop amplitudes at multicritical points

Abstract

We construct bosonic and fermionic matrix-vector models which describe orbifolded string worldsheets at a limit in which the dimension of the vector space and the matrix order are taken to infinity. We evaluate tree-level one-loop or multiloop amplitudes of these string worldsheets by means of Schwinger-Dyson equations and derive their expressions at the multicritical points. Some of these amplitudes resemble or are closely related to those of ordinary multicritical Hermitian matrix models by a constant factor, whereas some differ significantly.