A Connection between K3 Surfaces and the Conway Moonshine Module 公开

Abstract

In this paper, we survey an interesting duality between K3 surfaces and the Conway moonshine modules via Jacobi forms. K3 surfaces are studied extensively in the context of string compactification since they are manageable, yet non-trivial kind of Calabi-Yau manifold. An important topological invariant discovered by Witten in [1] is the elliptic genus. The elliptic genus of a K3 surface is a weak modular form of weight zero and index 1. In this text we show that a certain graded trace associated to the Conway moonshine module coincides with the K3 elliptic genus.

Table of Contents

Section 1: Introduction…………………………………………………………………..1

Section 2: Background …………………………………………………………………..1

Section 3: Main Theorem………………………………………………………………14

Section 4: References……………………………………………………………………19

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Mathematics
关键词	Moonshine Conway Group K3 Surfaces
Committee Chair / Thesis Advisor	Duncan, John, Emory University
Committee Members	Zureick-Brown, David, Emory University Srivastava, Ajit, Emory University

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