Noncommutative probability, matrix models, and quantum orbifold geometry

TL;DR

This paper explores the connection between noncommutative probability of type B, fermionic matrix-vector models, and orbifolded string worldsheets, revealing new insights into their critical behavior and amplitudes.

Contribution

It introduces fermionic matrix-vector models as physical realizations of noncommutative probability of type B, linking them to orbifold string theories.

Findings

Fermionic matrix-vector models describe orbifolded string worldsheets.

Critical exponents match those of ordinary string worldsheets.

Renormalised amplitudes differ from non-orbifolded cases.

Abstract

Inspired by the intimate relationship between Voiculescu's noncommutative probability theory (of type A) and large-N matrix models in physics, we look for physical models related to noncommutative probability theory of type B. These turn out to be fermionic matrix-vector models at the double large-N limit. In the context of string theory, they describe different orbifolded string worldsheets with boundaries. Their critical exponents coincide with that of ordinary string worldsheets, but their renormalised tree-level one-boundary amplitudes differ.