Topological Holography

Abstract

We study a topological field theory in four dimensions on a manifold with boundary. A bulk-boundary interaction is introduced through a novel variational principle rather than explicitly. Through this scheme we find that the boundary values of the bulk fields act as external sources for the boundary theory. Furthermore, the full quantum states of the theory factorize into a single bulk state and an infinite number of boundary states labeled by loops on the spatial boundary. In this sense the theory is purely holographic. We show that this theory is dual to Chern-Simons theory with an external source. We also point out that the holographic hypothesis must be supplemented by additional assumptions in order to take into account bulk topological degrees freedom, since these are apriori invisible to local boundary fields.

LaTeX 10 pages, 1 figure using epsfig, typo in eqn.(15) corrected

References in corpus (4)

• Gauge Theory Correlators from Non-Critical String Theory
• The Holographic Bound in Anti-de Sitter Space
• Anti-de Sitter/CFT Correspondence in Three-Dimensional Supergravity
• Statistical Entropy and AdS/CFT Correspondence in BTZ Black Holes

Cited by in corpus (5)

• Conformal topological Yang-Mills theory and de Sitter holography
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography