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

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• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Late-time Structure of the Bunch-Davies De Sitter Wavefunction
• Conceptual Aspects of Gauge/Gravity Duality
• Disorder Operators in Chern-Simons-Fermion Theories
• Black hole microstates in AdS
• Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories
• Cosmological Shapes of Higher-Spin Gravity
• FRW and domain walls in higher spin gravity
• Emergent gravity from Eguchi-Kawai reduction
• de Sitter at all loops: the story of the Schwinger model
• Higher Spin de Sitter Hilbert Space
• Unitarity of Symplectic Fermion in $\alpha$-vacua with Negative Central Charge
• Late-time Structure of the Bunch-Davies FRW Wavefunction
• Instantons and the Hartle-Hawking-Maldacena Proposal for dS/CFT
• Cosmological solutions from 4D $N=4$ matter-coupled supergravity