Noncommutative aspects of open/closed strings via foliations

TL;DR

This paper explores the algebraic structures in string theory through noncommutative geometry of foliations, introducing string diagrammatics and their implications for Hochschild complexes and quantum chains.

Contribution

It introduces the concept of string diagrammatics within noncommutative geometry and analyzes their impact on Hochschild complexes and quantum chains in string theory.

Findings

Development of string diagrammatics in noncommutative geometry

New quantum chains for loop spaces derived from the framework

Stabilization results in the semi-simple case

Abstract

We give a brief summary of algebraic aspects of string theory arising in the noncommutative geometry setting of foliations called string diagrammatics which we introduced jointly with Bob Penner. We furthermore discuss how this gives rise to actions on the Hochschild complex of a Frobenius algebra. We then explain how this leads to new quantum chains for loop spaces and a stabilization in the semi--simple case.