The emergence of Einstein gravity from topological supergravity in $3+1$D

TL;DR

This paper demonstrates how Einstein gravity can emerge from a topological supergravity framework in 3+1 dimensions, where a small deformation leads to classical spacetime dynamics governed by Einstein's equations.

Contribution

It introduces a novel deformation of topological supergravity that results in the emergence of classical Einstein gravity from a topological quantum field theory.

Findings

Deformation parameter $mbda$ induces instability in the TQFT.

Emergence of classical metric obeying Einstein equations.

Classical spacetime ceases beyond the Planck scale.

Abstract

The topological aspects of Einstein gravity suggest that topological invariance could be a more profound principle in understanding quantum gravity. In this work, we explore a topological supergravity action that initially describes a universe without Riemann curvature, which seems trivial. However, we made a surprising discovery by introducing a small deformation parameter $\lambda$, which can be regarded as an AdS generalization of supersymmetry (SUSY). We find that the deformed topological quantum field theory (TQFT) becomes unstable at low energy, resulting in the emergence of a classical metric, whose dynamics are controlled by the Einstein equation. Our findings suggest that a quantum theory of gravity could be governed by a UV fixed point of a SUSY TQFT, and classical spacetime ceases to exist beyond the Planck scale.