Surveys in Differential Geometry

Volume 15 (2010)

Spin structures and superstrings

Pages: 99 – 130



Jacques Distler (Theory Group, Department of Physics, Texas Cosmology Center, University of Texas, Austin, Tx., U.S.A.)

Daniel S. Freed (Department of Mathematics, University of Texas, Austin, Tx., U.S.A.)

Gregory W. Moore (NHETC and Department of Physics and Astronomy, Rutgers University, Piscataway, N.J., U.S.A.)


In superstring theory spin structures are present on both the 2-dimensional worldsheet and 10-dimensional spacetime. We present a new proposal for the $B$-field in superstring theory and demonstrate its interaction with worldsheet spin structures. Our formulation generalizes to orientifolds, where various twistings appear. A special case of the orientifold worldsheet $B$-field amplitude is a $KO$-theoretic construction of the $\zmod8$-valued Kervaire invariant on \pinm\ surfaces.

Published 1 January 2010