Conformal Covariance Subalgebras

TL;DR

This paper characterizes conformal inclusions of chiral current algebras using Lie algebraic methods, proving a longstanding conjecture and exploring structures of conformal covariance subalgebras and coset current algebras.

Contribution

It provides a direct Lie algebraic characterization of conformal inclusions and proves Schellekens and Warner's conjecture using quantum field theoretic arguments.

Findings

Proved a longstanding conjecture on conformal inclusions.

Characterized conformal covariance subalgebras.

Explored structures of coset current algebras.

Abstract

We give a direct Lie algebraic characterisation of conformal inclusions of chiral current algebras associated with compact, reductive Lie algebras. We use straightforward quantum field theoretic arguments and prove a long standing conjecture of Schellekens and Warner on grounds of unitarity and positivity of energy. We explore the structures found to characterise ``conformal covariance subalgebras'' and ``coset current algebras''.