Local algebra and string theory

TL;DR

This paper explores the mathematical structure of the $eta ext{-}gamma$ system in string theory, using local algebra to address questions about state spaces, dualities, and partition functions.

Contribution

It introduces a rigorous mathematical framework for the $eta ext{-}gamma$ system on pure spinor cones, connecting local algebra with string theory concepts.

Findings

Provides a definition of the space of states for the $eta ext{-}gamma$ system

Offers insights into dualities and pairings in string theory

Suggests approaches to computing the partition function

Abstract

The $\beta\gamma$ system on the cone of pure spinors is an integral part of the string theory developed by N. Berkovits. This $\beta\gamma$ system offer a number of questions for pure mathematicians: what is a precise definition of the space of states of the theory? Is there a mathematical explanations for various dualities (or pairings) predicted by physicists? Can a formula for partition function be written? To help me to answer these questions I use local algebra in an essential way.