The Euclidean path integral on elliptic de Sitter defines a no-boundary density matrix whose entropies reduce to vertex operator correlators on non-orientable surfaces, with a one-dimensional global Hilbert space but nontrivial observer Fock spaces.
Universal entropy of conformal critical theories on a Klein bottle
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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.
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No boundary density matrix in elliptic de Sitter dS/$\mathbb{Z}_2$
The Euclidean path integral on elliptic de Sitter defines a no-boundary density matrix whose entropies reduce to vertex operator correlators on non-orientable surfaces, with a one-dimensional global Hilbert space but nontrivial observer Fock spaces.