nLab discrete torsion





Special and general types

Special notions


Extra structure



Differential cohomology



What is known in the literature as discrete torsion (Vafa 86) are phenomena of equivariant ordinary differential cohomology, specifically of circle 2-bundles with connection (e.g. represented as bundle gerbes) modelling the B-field in string theory over orbifold spacetimes (Sharpe 99) and of circle 3-bundles with connection (e.g. represented as bundle 2-gerbes) modelling the supergravity C-field on orbifolds (Sharpe 00), as in M-theory on G2-manifolds with ADE-singularities.


For the B-field

Early discussion of classification in 2d CFTs includes

and more specifically for orbifolds in string theory in

The identification of discrete torsion in type II string theory as a choice of orbifold equivariance on a principal 2-bundle/bundle gerbe is due to

based on

In relation to twisted Chen-ruan orbifold cohomology:

See also

The case of heterotic string theory is discussed in

For the C-field

The higher version of discrete torsion for circle 3-bundles describing the supergravity C-field is discussed in

and applied to discussion of black M2-brane worldvolume field theory (BLG model/ABJM model, see at fractional M2-brane) in

See also at finite subgroup of SU(2) the section on group cohomology.

Last revised on December 21, 2021 at 10:36:39. See the history of this page for a list of all contributions to it.