Elliptic Genera and q-Series Development in Analysis, String Theory, and N=2 Superconformal Field Theory

TL;DR

This paper explores the mathematical structures underlying string theory and superconformal field theories, focusing on elliptic genera, spectral functions, and their modular properties, to deepen understanding of theoretical physics models.

Contribution

It introduces a novel analysis of Ruelle spectral functions and their relation to elliptic genera in N=2 theories, linking spectral functions with string partition functions and modular transformations.

Findings

Derived functional equations for spectral functions

Analyzed modular transformation laws of elliptic genera

Connected spectral functions with string theory models

Abstract

In this article we examine the Ruelle type spectral functions $\cR(s)$,which define an overall description of the content of the work. We investigate the Gopakumar-Vafa reformulation of the string partition functions, describe the N=2 Landau-Ginzburg model in terms of Ruelle type spectral functions. Furthermore, we discuss the basic properties satisfied by elliptic genera in N=2 theories, construct the functional equations for $\cR(s)$, and analyze the modular transformation laws for the elliptic genus of the Landau-Ginzburg model and study their properties in details.