Surveys in Differential Geometry
Volume 15 (2010)
Spin structures and superstrings
Pages: 99 – 130
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.