On a Residue Representation of Deformation, Koszul and Chiral Rings

TL;DR

This paper introduces a residue-based framework for representing deformation and chiral rings in Calabi-Yau models, linking algebraic structures with physical BRST analysis.

Contribution

It provides a residue-theoretic approach to deformation and chiral rings, generalizing polynomial deformations and connecting to BRST analysis.

Findings

Residue representation for massless matter fields

Generalization of polynomial deformations

Connection to BRST analysis of constrained systems

Abstract

A residue-theoretic representation is given for massless matter fields in (quotients) of (weighted) \CY\ complete intersection models and the corresponding chiral operators in \LGO{s}. The well known polynomial deformations are thus generalized and the universal but somewhat abstract Koszul computations acquire a concrete realization and a general but more heuristic reinterpretation. A direct correspondence with a BRST-type analysis of constrained systems also emerges naturally.