Emergent gravity from Eguchi-Kawai reduction

Abstract

Holographic theories with a local gravitational dual have a number of striking features. Here I argue that many of these features are controlled by the Eguchi-Kawai mechanism, which is proposed to be a hallmark of such holographic theories. Higher-spin holographic duality is presented as a failure of the Eguchi-Kawai mechanism, and its restoration illustrates the deformation of higher-spin theory into a proper string theory with a local gravitational limit. AdS/CFT is used to provide a calculable extension of the Eguchi-Kawai mechanism to field theories on curved manifolds and thereby introduce "topological volume independence." Finally, I discuss implications for a general understanding of the extensivity of the Bekenstein-Hawking-Wald entropy.

29 pages plus appendices, v2-v3: references added and typos corrected

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Cited by in corpus (15)

• Holography at finite cutoff with a $T^2$ deformation
• BCFT entanglement entropy at large central charge and the black hole interior
• Global symmetry, Euclidean gravity, and the black hole information problem
• Entanglement in De Sitter Space
• Einstein gravity from ANEC correlators
• Reflected entropy in random tensor networks
• Phases of scrambling in eigenstates
• Modular invariance on $S^1\times S^3$ and circle fibrations
• Parity and the modular bootstrap
• Detachable circles and temperature-inversion dualities for CFT${}_d$
• Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
• Sub-AdS Scale Locality in AdS${}_3$/CFT${}_2$
• Phase Transitions and Stability of Eguchi-Hanson-AdS Solitons
• Sparseness bounds on local operators in holographic $CF{T}_d$
• A symmetry principle for emergent spacetime