Existence and implications of exotic twisted spinors

Determine whether spinor fields that simultaneously realize an exotic spinor structure—i.e., sections of spinor bundles associated with nonequivalent spin structures on multiply connected manifolds—and twisted boundary conditions (anti-periodic boundary conditions along a compact dimension) exist, and characterize the physical consequences of such exotic twisted spinors, taking into account the vanishing-connection constraint on the Dirac operator that underlies twisted fields in settings such as S^1 × R^3.

Background

Twisted spinor fields, typically defined by anti-periodic boundary conditions along compact directions, were extensively studied in backgrounds like S^1 × R^3. In many of these settings the spacetime also admits nonequivalent spin structures, leading to exotic spinors—spinor fields arising from distinct, inequivalent spin structures tied to nontrivial topology.

The paper notes that combining twisting with exoticity is challenging because twisted fields are often enabled by a restrictive, vanishing-connection constraint on the Dirac operator. Despite this overlap of contexts that admit both twisted fields and exotic spinor structures, it has not been established whether spinors that are simultaneously exotic and twisted exist or what their physical consequences would be.