Simple currents versus orbifolds with discrete torsion -- a complete classification

Details Simple currents versus orbifolds with discrete torsion -- a complete classification Simple currents versus orbifolds with discrete torsion -- a complete classification

1993-06-28

arxiv.org/abs/hep-th/9306145v1

Nucl.Phys. B411 (1994) 97-121

Physics

High Energy Physics

High Energy Physics - Theory

28 pages

Scientific paper

10.1016/0550-3213(94)90055-8

We give a complete classification of all simple current modular invariants, extending previous results for $(\Zbf_p)^k$ to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this end, we find a one-to-one correspondence between simple current invariants and subgroups of the center with discrete torsions. As a by-product, we prove the conjectured monodromy independence of the total number of such invariants. The orbifold approach works in a straightforward way for symmetries of odd order, but some modifications are required to deal with symmetries of even order. With these modifications the orbifold construction with discrete torsion is complete within the class of simple current invariants. Surprisingly, there are cases where discrete torsion is a necessity rather than a possibility.

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