Induced topological gravity and anomaly inflow from Kähler-Dirac fermions in odd dimensions

Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions

“…In odd dimensions the mapping to spinors is more subtle -the matrix representation of the D = 2n + 1 dimensional Kähler-Dirac theory requires employing gamma matrices of size 2 n+1[23]. The degrees of freedom carried by the resultant matrix fermion are then reduced by a factor of two using the projectors described in section 3.…”