Quasi-quantum groups from strings

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 $D_ω[G]$, introduced in the context of conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche, with $ω$ a 3-cocycle determined by a series of cohomological equations in a tricomplex combining de Rham, uCech and group cohomologies. We further illustrate some properties of the quasi-quantum group from a string theoretical point of view.

10 pages, 8 figures, talk given at the conference "Noncommutative Geometry and Physics", Orsay April 2007