Jordan cells in logarithmic limits of conformal field theory

TL;DR

This paper explores how taking limits of conformal field theories can produce logarithmic conformal field theories with complex Jordan cell structures, extending previous work and analyzing limits of three-point functions and characters.

Contribution

It introduces a general method for constructing logarithmic conformal field theories with arbitrary Jordan cell rank via limiting procedures, expanding on prior rank-two cases.

Findings

Limits of minimal models produce logarithmic theories with Jordan cells of any rank.

Three-point functions in the limits are consistent with known logarithmic CFT results.

Characters of quasi-rational representations emerge as limits of Virasoro characters.

Abstract

It is discussed how a limiting procedure of conformal field theories may result in logarithmic conformal field theories with Jordan cells of arbitrary rank. This extends our work on rank-two Jordan cells. We also consider the limits of certain three-point functions and find that they are compatible with known results. The general construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field theory. Characters of quasi-rational representations are found to emerge as the limits of the associated irreducible Virasoro characters.