Universal Entropy of Conformal Critical Theories on a Klein Bottle

We show that rational conformal field theories in 1 + 1 dimensions on a Klein bottle, with a length L and width beta, satisfying L >> beta, have a universal entropy. This universal entropy depends 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 the characterization of conformal critical theories. The result is checked against exact calculations in quantum spin-1/2 XY and Ising chains.