Chern-Simons-Ghost Theories and de Sitter Space

TL;DR

This paper investigates Chern-Simons-ghost theories in the large N limit, revealing a mapping to ordinary Chern-Simons-matter theories and extending bosonization duality, with implications for holography and de Sitter space.

Contribution

It demonstrates a N to -N mapping in large N perturbation theory and extends bosonization duality to ghost-like matter theories on 3, with analysis of partition functions related to de Sitter holography.

Findings

N  -N mapping in large N limit

Bosonization duality extends to ghost theories on 3

Partition functions relate to de Sitter wavefunction

Abstract

We explore Chern-Simons theories coupled to fundamental ghost-like matter in the large $N$ limit at 't Hooft coupling $\lambda$. These theories have been conjectured to be holographically dual to parity-violating, asymptotically dS$_4$ universes with a tower of light higher-spin fields. On $\mathbb{R}^3$, to all orders in large-$N$ perturbation theory, we show that Chern-Simons-ghost theories are related to ordinary Chern-Simons-matter theories by mapping $N \rightarrow - N$ and keeping $\lambda$ fixed. Consequently, the bosonization duality of ordinary Chern-Simons-matter theories extends to a bosonization duality of Chern-Simons-ghost theories on $\mathbb R^3$. On $S^1 \times S^2$, in the small-$S^1$ limit, neither $N \rightarrow -N$ nor bosonization hold, as we show by extensively studying large-$N$ saddles of the theories with both ghost and ordinary matter. The partition functions we compute along the way can be viewed as pieces of the late-time Hartle-Hawking wavefunction for the bulk dS$_4$ gravity theories.