On Tachyons in Generic Orbifolds of $\BC^r$ and Gauged Linear Sigma Models

TL;DR

This paper investigates Gauged Linear Sigma Models for orbifolds of complex spaces, analyzing their phases and deriving sigma model Lagrangians based on toric geometry, with a focus on tachyonic singularities.

Contribution

It provides explicit sigma model Lagrangians for orbifolds of a2^r/\u03b3 and analyzes their phase structure, highlighting the role of toric geometry in these models.

Findings

Derived multi-parameter sigma model Lagrangians from toric data.

Analyzed phase structures of orbifolds of a2^r.

Discussed tachyonic aspects of orbifold singularities.

Abstract

We study some aspects of Gauged Linear Sigma Models corresponding to orbifold singularities of the form $\BC^r/\Gamma$, for $r=2,3$ and $\Gamma = \BZ_n$ and $\BZ_n\times \BZ_m$. These orbifolds might be tachyonic in general. We compute expressions for the multi parameter sigma model Lagrangians for these orbifolds, in terms of their toric geometry data. Using this, we analyze some aspects of the phases of generic orbifolds of $\BC^r$.