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discrete torsion

Idea

What is known in the literature as discrete torsion are phenomena of equivariant ordinary differential cohomology, specifically of circle 2-bundles with connection modelling the B-field in string theory over orbifold base spaces.

References

Discussion of classification includes

• Maximilian Kreuzer, A. N. Schellekens, Simple currents versus orbifolds with discrete torsion – a complete classification, Nucl.Phys. B411 (1994) 97-121 (arXiv:hep-th/9306145)

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

• Eric Sharpe,

  Discrete Torsion and Gerbes I (arXiv:hep-th/9909108)

  Discrete Torsion and Gerbes II (arXiv:hep-th/9909120)

  Discrete Torsion, Quotient Stacks, and String Orbifolds (arXiv:math/0110156)

Generalization to heterotic string theory is discussed in

• Eric Sharpe Discrete Torsion in Perturbative Heterotic String Theory, Phys.Rev. D68 (2003) 126005 (arXiv:hep-th/0008184)

and the analog for the C-field 2-gerbe in M-theory in

• Eric Sharpe, Analogues of Discrete Torsion for the M-Theory Three-Form, Phys.Rev. D68 (2003) 126004 (arXiv:hep-th/0008170)

See also

• Cumrun Vafa, Edward Witten, On Orbifolds with Discrete Torsion, J.Geom.Phys.15:189-214,1995 (arXiv:hep-th/9409188)