On conformal Jordan cells of finite and infinite rank

TL;DR

This paper explores the construction and reduction of conformal Jordan cells of finite and infinite rank, revealing how finite cells relate to a universal infinite cell and how contractions can lower rank.

Contribution

It introduces methods to construct infinite rank conformal Jordan cells and reduce finite rank cells via a contraction-like procedure, linking finite and infinite structures.

Findings

Infinite rank conformal Jordan cells can be constructed and related to finite rank cells.

Finite conformal Jordan cells can be obtained from a universal infinite cell.

A contraction-like procedure reduces the rank of conformal Jordan cells.

Abstract

This work concerns in part the construction of conformal Jordan cells of infinite rank and their reductions to conformal Jordan cells of finite rank. It is also discussed how a procedure similar to Lie algebra contractions may reduce a conformal Jordan cell of finite rank to one of lower rank. A conformal Jordan cell of rank one corresponds to a primary field. This offers a picture in which any finite conformal Jordan cell of a given conformal weight may be obtained from a universal covering cell of the same weight but infinite rank.