More Curiosities at Effective c = 1

TL;DR

This paper explores the structure of the moduli space of rational conformal quantum field theories with effective central charge c_eff = 1, revealing a dense fractal set of non-unitary theories linked to the modular group.

Contribution

It characterizes the moduli space of these theories, showing unitary theories form a manifold while non-unitary ones form a dense fractal set related to the modular group.

Findings

Unitary theories form a manifold in the moduli space.

Non-unitary theories form a dense fractal set.

Non-unitary points correspond to elements of the modular group.

Abstract

The moduli space of all rational conformal quantum field theories with effective central charge c_eff = 1 is considered. Whereas the space of unitary theories essentially forms a manifold, the non unitary ones form a fractal which lies dense in the parameter plane. Moreover, the points of this set are shown to be in one-to-one correspondence with the elements of the modular group for which an action on this set is defined.