On the topological and crosscap entropies in non-oriented RCFTs

Abstract

We establish a relation between the boundary and the topological entropies for the conformal minimal models in some of the simplest models of the unitary A-A series. We show that in these models the boundary entropy is a difference of topological entropies. Furthermore, we define the crosscap entropy as the analog to the boundary entropy in non-oriented theories. The crosscap entropy is defined as the logarithm of the degeneracy of the ground state due to the presence of crosscaps and it can be expressed in terms of the crosscap coefficients. This crosscap entropy has not an explicit relation to the topological entropy as the boundary entropy. However, we propose a new quantity, $\hat{S}=\ln P_{0i}$ defined in terms of the modular transformation $P$ between the open and closed channel of the Möbius partition function. With this quantity, the crosscap entropy can be regarded as a difference of entropies, very similar to the boundary entropy. We also compute the left-right entanglement entropy (LREE) for crosscap states and we express it in terms of $\hat{S}$. An explicit example of the LREE of the crosscap state in Wess-Zumino-Witten is carried out

24 pages, change of title, major changes along the article, subsection 2.2 was added and section 3 has completely changed. New references were added

References in corpus (10)

• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Left-Right Entanglement Entropy of Boundary States
• Universal entropy of conformal critical theories on a Klein bottle
• Entanglement entropy at CFT junctions
• Holography on Non-Orientable Surfaces
• Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
• Duality and Mock Modularity
• Conformal Thermal Tensor Network and Universal Entropy on Topological Manifolds
• Left-Right Entanglement Entropy, D-Branes, and Level-rank duality

Cited by in corpus (3)

• Crosscap States in Integrable Field Theories and Spin Chains
• Universal scaling of Klein bottle entropy near conformal critical points
• Extracting the Luttinger parameter from a single wave function