Résume | The Landau-Ginzburg A-model of the quintic threefold has a description in terms of higher spin bundles on stable curves. In genus zero the invariants/correlators of the closed r-spin theory are given by integration of the top Chern class of the Witten bundle over the moduli space of stable curves. By allowing a new twist equal to -1 at one of the marked points, Alexandr Buryak, Emily Clader and Ran Tessler found a rank one extension of the closed r-spin theory in genus zero in 2017. After having a look at this extension, we will see that integration of the fifth power of this top Chern class gives an extension of the Fan-Jarvis-Ruan-Witten (FJRW) theory of the quintic threefold in genus zero. In order to calculate the new invariants, we will mimick the work of Alessandro Chiodo and Yongbin Ruan from 2008 and introduce the Givental formalism. I will sketch how Chiodo's Grothendieck-Riemann-Roch formula still provides us with a symplectic transformation of the twisted Givental cone. An extension of the I-function will arise in the non-equivariant limit of the twisted invariants. This extended I-function contains a new term already known as the semi-period. It is a solution of an inhomogeneous Picard-Fuchs equation with a constant inhomogeneity.
This is work in progress. |