On Homological and Homotopical Algebra of Supersymmetries and Integrability in String Theory

TL;DR

This paper explores a category theory framework for supersymmetries and integrability in string theory, focusing on homological and homotopical algebra of Calabi-Yau supermanifolds and stacks.

Contribution

It introduces a novel homological and homotopical algebra approach to analyze supersymmetries and integrability in string theory using Calabi-Yau supermanifolds.

Findings

Framework for supersymmetries in supermanifolds

Homological algebra approach to integrability

Application to open and closed string theory

Abstract

The text contains introduction and preliminary definitions and results to my talk on category theory description of supersymmetries and integrability in string theory. In the talk I plan to present homological and homotopical algebra framework for Calabi-Yau supermanifolds and stacks in open and closed string theory. In the framework we investigate supersymmetries and integrability.