Twisted Gromov-Witten r-spin potential and Givental's quantization

Understand

The universal curve p:C->\Mbar over the moduli space \Mbar of stable r-spin maps to a target K\"ahler manifold X carries a universal spinor bundle L->C.

• Therefore the moduli space \Mbar itself carries a natural K-theory class Rp_*L.
• We introduce a twisted r-spin Gromov-Witten potential of X enriched with Chern characters of Rp_*L.
• We show that the twisted potential can be reconstructed from the ordinary r-spin Gromov-Witten potential of X via an operator that assumes a particularly simple form in Givental's quantization formalism.