Duality Group for Calabi-Yau 2-Moduli Space

TL;DR

This paper introduces an efficient method to compute the duality group of a specific Calabi-Yau 2-moduli space, revealing it as a 3D representation of a central extension of the braid group B_5.

Contribution

It provides a novel computational approach to determine the duality group for a class of Calabi-Yau moduli spaces, linking it to braid group representations.

Findings

Duality group is a 3D representation of a central extension of B_5.

Method simplifies the computation of duality groups for Calabi-Yau moduli.

Identifies the structure of the duality group for a specific two-moduli deformation.

Abstract

We present an efficient method for computing the duality group $\Gamma$ of the moduli space \cM for strings compactified on a Calabi-Yau manifold described by a two-moduli deformation of the quintic polynomial immersed in $\CP(4)$, $\cW={1\over5}(\iy_1^5+\cdots+\iy_5^5)-a\,\iy_4^3 \iy_5^2 -b\, \iy_4^2 \iy_5^3$. We show that $\Gamma$ is given by a $3$--dimensional representation of a central extension of $B_5$, the braid group on five strands.