The Cosmological Constant: A Categorical View

TL;DR

This paper explores the cosmological constant through a category-theoretic lens, revealing how quantum spacetime structures and Einstein gravity emerge from higher category frameworks, connecting recent advances in mathematical physics.

Contribution

It introduces a novel categorical perspective on the cosmological constant, demonstrating how Einstein gravity and quantum spacetime structures can be derived from higher categories.

Findings

Categorical patterns underpin cosmological constant results.

Emergence of Einstein gravity from 2-tuply monoidal 2-categories.

Integration of Vertex Operator Algebras and 4-manifolds into the framework.

Abstract

Some theoretic results related to the cosmological constant, obtained in the 80's and 90's of last century, are reviewed. These results exhibit some interesting underlying pattern when viewed from a category-theoretic perspective. In doing this, we illustrate how Baez and Dolan's Periodic Table of $k$-tuply monoidal $n$-categories can serve as a basic framework of a quantum spacetime structure. Explicitly, we show how Einstein gravity (with the cosmological constant turned on) emerges when we de-categorify certain $2$-tuply monoidal $2$-categories properly, as Crane proposed a long time ago. In particular, we find that some recent work on Vertex Operator Algebras and 4-manifolds fits nicely into this framework.