String Duality and a New Description of the E ₆ Singularity

Abstract

We discuss a new type of Landau-Ginzburg potential for the E ₆ singularity of the form $W = const + \left( {{Q_1}\left( x \right) + {P_1}\left( x \right)\sqrt {{P_2}\left( x \right)} } \right)/{x^3}$ which featured in a recent study of heterotic/type II string duality. Here Q1, P1 and P2 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.