A Connection between K3 Surfaces and the Conway Moonshine Module Público
Zhang, Qiyu (Spring 2020)
Published
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
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