C_2-cofiniteness of cyclic-orbifold models

TL;DR

This paper proves that for a certain class of algebraic structures called vertex operator algebras, taking fixed points under a solvable automorphism group preserves a property called C_2-cofiniteness, supporting orbifold theory.

Contribution

It establishes that fixed point subalgebras under finite solvable automorphism groups retain C_2-cofiniteness, confirming a conjecture in orbifold theory.

Findings

Fixed point subalgebras are C_2-cofinite under solvable automorphism groups.

Provides rigorous proof for orbifold conjecture in this context.

Supports mathematical foundation of orbifold models with solvable symmetry groups.

Abstract

We prove an orbifold conjecture for a solvable automorphism group. Namely, we show that if V is a C_2-cofinite simple vertex operator algebra and G is a finite solvable automorphism group of V, then the fixed point vertex operator subalgebra V^G is also C_2-cofinite. This offers a mathematically rigorous background to orbifold theories of finite type with solvable automorphism groups.