Bundle gerbes with connection and their modules play an important role in the theory of two-dimensional sigma models with a background Wess–Zumino flux: their holonomy determines the contribution of the flux to the Feynman amplitudes of classical fields. We discuss additional structures on bundle gerbes and gerbe modules needed in similar constructions for orientifold sigma models describing closed and open strings.
"Bundle gerbes for orientifold sigma models." Adv. Theor. Math. Phys. 15 (3) 621 - 687, June 2011.