Chiral De Rham complex over locally complete intersections

TL;DR

This paper introduces a derived chiral De Rham complex for locally complete intersections, linking it to dg vertex algebras and differential operators, with applications to Landau-Ginzburg models.

Contribution

It constructs a new derived chiral De Rham complex over locally complete intersections and establishes Morita equivalence with dg algebras of differential operators.

Findings

The dg vertex algebra for a fat point is derived rational.

The construction generalizes Illusie and Bhatt's results.

Attaches dg vertex algebras to graded rings.

Abstract

We define a version of a derived chiral De Rham complex over a locally complete intersection, thereby "chiralizing" a result by Illusie and Bhatt. A similar construction attaches to a graded ring a dg vertex algebra, which we prove to be Morita equivalent to a dg algebra of differential operators. For example, the dg vertex algebra associated to a fat point, which also arises in the Landau-Ginzburg model, is shown to be derived rational.