Topological and Geometric Universal Thermodynamics in Conformal Field Theory

Abstract

Universal thermal data in conformal field theory (CFT) offer a valuable means for characterizing and classifying criticality. With improved tensor network techniques, we investigate the universal thermodynamics on a nonorientable minimal surface, the crosscapped disk (or real projective plane, ${\mathbb{RP}}^2$). Through a cut-and-sew process, ${\mathbb{RP}}^2$ is topologically equivalent to a cylinder with rainbow and crosscap boundaries. We uncover that the crosscap contributes a fractional topological term $\frac{1}{2}\ln k$ related to nonorientable genus, with $k$ a universal constant in two-dimensional CFT, while the rainbow boundary gives rise to a geometric term $\frac{c}{4}\ln \beta$, with $\beta$ the manifold size and $c$ the central charge. We have also obtained analytically the logarithmic rainbow term by CFT calculations, and discuss its connection to the renowned Cardy-Peschel conical singularity.

4 pages + references, 7 figures, 2 tables, supplementary material; published version

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Cited by in corpus (6)

• Critical properties of the two-dimensional $q$-state clock model
• Klein bottle entropy of compactified boson conformal field theory
• Universal scaling of Klein bottle entropy near conformal critical points
• Extracting the Luttinger parameter from a single wave function
• Crosscap states and duality of Ising field theory in two dimensions
• Tensor network simulations for nonorientable surfaces