1999/09/15 by Eric Sharpe, Eric R. Sharpe, Sharpe, Eric R. · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th #math.DG
paper · pdf · doi:10.48550/arxiv.hep-th/9909108
40 pages, must LaTeX 3x; v2: typos fixed and other minor upgrades; v3: more minor upgrades
openalex publication_date 1999/09/15 · arxiv created 2000/08/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this technical note we give a purely geometric understanding of discrete torsion, as an analogue of orbifold Wilson lines for two-form tensor field potentials. In order to introduce discrete torsion in this context, we describe gerbes and the description of certain type II supergravity tensor field potentials as connections on gerbes. Discrete torsion then naturally appears in describing the action of the orbifold group on (1-)gerbes, just as orbifold Wilson lines appear in describing the action of the orbifold group on the gauge bundle. Our results are not restricted to trivial gerbes -- in other words, our description of discrete torsion applies equally well to compactifications with nontrivial H-field strengths. We also describe a speciric program for rigorously deriving analogues of discrete torsion for many of the other type II tensor field potentials, and we are able to make specific conjectures for the results.