Variance of the exponents of orbifold Landau-Ginzburg models

TL;DR

This paper derives a formula for the variance of exponents in orbifold Landau-Ginzburg models with weighted homogeneous polynomials and diagonal group actions, advancing understanding of their spectral properties.

Contribution

It introduces a novel formula for the variance of exponents in orbifold Landau-Ginzburg models with specific symmetry groups, filling a gap in spectral analysis.

Findings

Derived a formula for the variance of exponents

Applied the formula to weighted homogeneous polynomials

Enhanced understanding of spectral properties in orbifold models

Abstract

We prove a formula for the variance of the set of exponents of a non-degenerate weighted homogeneous polynomial with an action of a diagonal subgroup of ${\rm SL}_n(\CC)$.