# nLab discrete torsion

Contents

cohomology

### Theorems

#### Differential cohomology

differential cohomology

# Contents

## Idea

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.

## References

### 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