Universal entropy of conformal critical theories on a Klein bottle

TL;DR

This paper demonstrates that rational conformal field theories on a Klein bottle possess a universal entropy linked to their topological properties, which can be used to characterize conformal critical points.

Contribution

It introduces a universal entropy for conformal theories on a Klein bottle, connecting it to quantum dimensions and providing a practical extraction method.

Findings

Universal entropy depends on quantum dimensions of primary fields.

The entropy can be extracted via ratio of Klein bottle and torus partition functions.

Results validated in quantum spin-1/2 XY and Ising chains.

Abstract

We show that rational conformal field theories in 1+1 dimensions on a Klein bottle, with length $L$ and width $\beta$, satisfying $L \gg \beta$, have a universal entropy. This universal entropy is a topological invariant depending on the quantum dimensions of the primary fields and can be accurately extracted by taking a proper ratio between the Klein bottle and torus partition functions, enabling a characterization of conformal critical theories. The result is checked against exact calculations in quantum spin-1/2 XY and Ising chains.