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.

Figures (2)

• Figure 1: Left: A tree-level Witten diagram, which contributes at leading order in $N$ to the nine-point function. It is constructed out of $M=9$ bulk-to-boundary propagators and $n=5$ bulk-to-bulk propagators. Since it is a contribution at tree level, there are $6=n+1$ interaction vertices. There are many more diagrams contributing at this order. Right: A loop-level Witten diagram, which contributes at first subleading order in $N$ to the nine-point function. It is constructed out of $M=9$ bulk-to-boundary propagators and $n=8$ bulk-to-bulk propagators. There are $8\neq n+1$ interaction vertices. There are again many more diagrams contributing at this order.
• Figure 2: Left: A tree-level Witten diagram, which contributes at leading order in $N$ to the four-point function. It is constructed out of $M=4$ bulk-to-boundary propagators and $n=1$ bulk-to-bulk propagator. Since it is a contribution at tree level, there are $2=n+1$ interaction vertices. There are more diagrams contributing at this order, including the one with the four bulk-to-boundary propagators meeting at a single interaction vertex in the interior.