Chiral Observables and Modular Invariants

TL;DR

This paper explores the equivalence of different definitions of chiral observables in 2D conformal theories, analyzing their representation theory and modular invariance properties without assuming SL(2,Z) symmetry, and initiates classification efforts.

Contribution

It demonstrates the equivalence of various chiral observable definitions and studies their representation theory, advancing understanding of modular invariants without relying on SL(2,Z) assumptions.

Findings

Chiral observables definitions are equivalent in 2D theories.

Representation theory exhibits characteristics similar to modular invariants.

Initial steps towards classification of these observables are presented.

Abstract

Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general characteristics of modular invariant partition functions, although SL(2,Z) transformation properties are not assumed. First steps towards classification are made.