Chern-Simons-Ghost Theories and de Sitter Space

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 $N\to -N$ 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 $N\to -N$ 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.

27 pages + appendices, 6 figures

References in corpus (7)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Higher Spins in AdS and Twistorial Holography
• AdS_4/CFT_3 Construction from Collective Fields
• Holographic dual of free field theory
• Chern-Simons-Fermion Vector Model with Chemical Potential
• Singlet Vector Models on Lens Spaces

Cited by in corpus (5)

• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Cosmological Shapes of Higher-Spin Gravity
• Higher Spin de Sitter Hilbert Space
• Late-time Structure of the Bunch-Davies FRW Wavefunction
• Instantons and the Hartle-Hawking-Maldacena Proposal for dS/CFT