Trace maps on chiral Clifford algebras for the rank two fermionic vertex operator superalgebra

For a holomorphic vector bundle $F$ of rank $r$ on a smooth Riemann surface $X$ we construct a trace map on the chiral homology of the chiral Clifford algebra $\CE$ attached to the purely odd bundle $E=Π(F\oplus F^\vee\otimesω_X)$. It is the chiral-algebraic realization of the rank two fermion