Dualities and Emergent Gravity: Gauge/Gravity Duality

TL;DR

This paper develops a framework linking dualities and emergence in physics, applies it to gauge/gravity dualities like AdS/CFT and Verlinde's scheme, and offers a new derivation of black hole entropy.

Contribution

It introduces a novel framework for understanding dualities and emergence, and applies it to gauge/gravity dualities, clarifying background-independence and providing a new entropy derivation.

Findings

AdS/CFT is background-independent in the minimalistic sense.

Verlinde's scheme aligns with extended background-independence.

A new derivation of black hole entropy from Verlinde's scheme.

Abstract

In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as 'isomorphism', cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and emergence (via coarse-graining). I apply this framework to gauge/gravity dualities, considering in detail three examples: AdS/CFT, Verlinde's scheme, and black holes. My main point about gauge/gravity dualities is that the theories involved, qua theories of gravity, must be background-independent. I distinguish two senses of background-independence: (i) minimalistic and (ii) extended. The former is sufficiently strong to allow for a consistent theory of quantum gravity; and AdS/CFT is background-independent on this account; while Verlinde's scheme best fits the extended sense. I argue that this extended sense should be applied with some caution: on pain of throwing the baby (general relativity) out with the bath-water (extended background-independence). Nevertheless, it is an interesting and potentially fruitful heuristic principle for quantum gravity theory construction. The interpretation of dualities is articulated in terms of: (i) epistemic and metaphysical commitments; (ii) parts vs. wholes. I then analyse the emergence of gravity in gauge/gravity dualities in terms of the two available conceptualisations of emergence; and I show how emergence in AdS/CFT and in Verlinde's scenario differ from each other. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on Verlinde's scheme; the derivation sheds light on several aspects of Verlinde's scheme and how it compares to Bekenstein's original calculation.