Universal entropy of conformal critical theories on a Klein bottle

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.