Quasi-quantum groups from strings

TL;DR

This paper constructs quasi-quantum groups from string theory on orbifolds with a Kalb-Ramond field, revealing their algebraic structure via cohomological methods and exploring their properties in a string context.

Contribution

It introduces a method to derive quasi-quantum groups from string orbifold models using cohomology, linking string theory with algebraic structures.

Findings

Operators generate the quasi-quantum group D_ω[G]

The 3-cocycle ω is determined by cohomological equations

Properties of the quasi-quantum group are analyzed in string theory context

Abstract

Motivated by string theory on the orbifold ${\cal M}/G$ in presence of a Kalb-Ramond field strength $H$, we define the operators that lift the group action to the twisted sectors. These operators turn out to generate the quasi-quantum group $D_{\omega}[G]$, introduced in the context of conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche, with $\omega$ a 3-cocycle determined by a series of cohomological equations in a tricomplex combining de Rham, \u{C}ech and group cohomologies. We further illustrate some properties of the quasi-quantum group from a string theoretical point of view.