Holographic Dual of Crosscap Conformal Field Theory

Abstract

We propose a holographic dual for 2D CFT defined on closed non-orientable manifolds, such as the real projective plane ${\mathbb{RP}}^2$ and the Klein bottle ${\mathbb{K}}^2$. Such CFT can be constructed by introducing antipodally identified cuttings, i.e. crosscaps, to a sphere and hence called crosscap CFT (XCFT). The gravity dual is AdS${}_3$ spacetime with dS${}_2$ end-of-the-world branes. In particular, the Lorentzian spacetime with a global dS${}_2$ brane is dual to the unitary time evolution of a crosscap state in CFT, post-selected on the CFT ground state. We compute the holographic ${\mathbb{RP}}^2$ partition function (or the $p$-function), one-point function, and ${\mathbb{K}}^2$ partition function, and see that they successfully reproduce the XCFT results. We also show a holographic $p$-theorem as an application.

17 pages + references, 4 figures; v3: details added

References in corpus (15)

• Holography from Conformal Field Theory
• An Algebra of Observables for de Sitter Space
• Codimension two holography for wedges
• Holography in de Sitter Space via Chern-Simons Gauge Theory
• A CFT Perspective on Gravitational Dressing and Bulk Locality
• Causal Structures and Nonlocality in Double Holography
• On the Page curve under final state projection
• Boundary Entropy Can Increase Under Bulk RG Flow
• Aspects of CFTs on Real Projective Space
• Universal entropy of conformal critical theories on a Klein bottle
• Zoo of holographic moving mirrors
• Crosscap States in Integrable Field Theories and Spin Chains
• AdS/BCFT from Conformal Bootstrap: Construction of Gravity with Branes and Particles
• Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature
• Universal scaling of Klein bottle entropy near conformal critical points

Cited by in corpus (8)

• Wormholes with Ends of the World
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Crosscap states and duality of Ising field theory in two dimensions
• Open-closed 3d gravity as a random ensemble
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States
• No boundary density matrix in elliptic de Sitter dS/${\mathbb{Z}}_2$
• Exact Quench Dynamics from Thermal Pure Quantum States
• Spacetime Bananas with EOW Branes and Spins