Discrete Torsion and Symmetric Products

Abstract

In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string theory making it essentially ``supersymmetric.'' The long strings of even length become fermionic (or ghosts), those of odd length bosonic. The partition function and elliptic genus can be described by a sum over stringy spin structures. The usual cubic interaction vertex is odd and nilpotent, so this construction gives rise to a DLCQ string theory with a leading quartic interaction.

latex, 18 pages

References in corpus (3)

• Lectures on Special Lagrangian Submanifolds
• A brief review of "little string theories"
• Permutation orbifolds

Cited by in corpus (11)

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• On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
• D1/D5 systems in $\mathcal{N}=4$ string theories
• Discrete torsion and twisted orbifold cohomology
• Discrete torsion, orbifold elliptic genera, and the chiral de Rham complex
• The orbifold transform and its applications
• Character relations and replication identities in 2d Conformal Field Theory
• Open Superstring on Symmetric Product