A New Description of the E_6 Singularity

TL;DR

This paper introduces a novel Landau-Ginzburg potential for the E_6 singularity, expanding the mathematical framework used in string theory dualities with detailed analysis of its properties.

Contribution

It presents a new form of the Landau-Ginzburg potential involving polynomial functions and demonstrates its consistency in describing the E_6 singularity.

Findings

New Landau-Ginzburg potential form for E_6

Detailed analysis confirms the potential's properties

Provides a consistent description of the E_6 singularity

Abstract

We discuss a new type of Landau-Ginzburg potential for the E_6 singularity of the form $W=const+(Q_1(x)+P_1(x)\sqrt{P_2(x)})/x^3$ which featured in a recent study of heterotic/typeII string duality. Here $Q_1,P_1$ and $P_2$ are polynomials of degree 15,10 and 10, respectively. We study the properties of the potential in detail and show that it gives a new and consistent description of the E_6 singularity.