New Gauged Linear Sigma Models for 8D HyperKahler Manifolds and Calabi-Yau Crystals

TL;DR

This paper introduces two novel gauged linear sigma models that describe 8D hyperKahler and Calabi-Yau manifolds, revealing new features in 3D Chern-Simons-matter theories and expanding the understanding of string theory compactifications.

Contribution

The paper presents new gauged linear sigma models for 8D hyperKahler and Calabi-Yau manifolds, including a novel approach for Calabi-Yau fourfolds as quotient spaces.

Findings

Models describe moduli spaces of hyperKahler and Calabi-Yau manifolds

Discovery of dynamical Fayet-Iliopoulos parameters in 3D theories

Identification of residual discrete gauge symmetries

Abstract

We propose two kinds of gauged linear sigma models whose moduli spaces are real eight-dimensional hyperKahler and Calabi-Yau manifolds, respectively. Here, hyperKahler manifolds have sp(2) holonomy in general and are dual to Type IIB (p,q)5-brane configurations. On the other hand, Calabi-Yau fourfolds are toric varieties expressed as quotient spaces. Our model involving fourfolds is different from the usual one which is directly related to a symplectic quotient procedure. Remarkable features in newly-found three-dimensional Chern-Simons-matter theories appear here as well, such as dynamical Fayet-Iliopoulos parameters, one dualized photon and its residual discrete gauge symmetry.