Index computations in FJRW theory

TL;DR

This paper calculates the index of the real Cauchy-Riemann operator in FJRW theory for smooth and cylindrical metrics, exploring relations with weighted Sobolev spaces and the Witten map.

Contribution

It provides explicit index computations in FJRW theory and analyzes the impact of different metrics on the linearized operator.

Findings

Index computed for smooth metric case.

Relation established between index and weights in Sobolev spaces.

Insights into the Witten map's linearized operator under cylindrical metric.

Abstract

We compute the index of the real Cauchy-Riemann operator defined in FJRW theory in case of the smooth metric. For the cylindrical metric, we study the relation between the index of the linearized operator of Witten map and weights in weighted Sobolev space.