# *ZOOM*[PhD Thesis Presentation] - Mr. Adrian David "Higher-spin holography in de Sitter space: horizon modes, black holes, and the boundary partition function"

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Presenter: Mr. Adrian David

Supervisor: Professor Shinobu Hikami

Co-supervisor: Professor Yasha Neiman

Unit: Mathematical and Theoretical Physics Unit

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Title: Higher-spin holography in de Sitter space: horizon modes, black holes, and the boundary partition function

Abstract:

In a strict sense, the problem of quantum gravity has been solved by string theory through the AdS/CFT correspondence in settings restricted to the spatial infinity of a universe with negative cosmological constant. Currently, there are outstanding questions of quantum gravity restricted to finite regions, as in the case of a positive cosmological constant where an observer only has access to partial information, as is the case for our observed universe.

De Sitter (dS) space is a natural toy model for quantum gravity in finite regions, however no satisfactory string-theoretic description of dS has been put forward. Recently, a new model for dS/CFT has been proposed with the Vasiliev bosonic higher-spin gravity as the bulk description, corresponding on CFT side to the Sp(2N) vector model.

In this body of work we review the recent progress concerning a higher-spin holographic duality over de Sitter space. The aim of the described approach is to construct a full holographic description of quantum gravity within the causal patch of a de Sitter observer. In particular, we focus on issues related to (i) cosmological horizon modes, (ii) black hole wordlines, and (iii) the boundary CFT partition function .

(i) We introduce [1] a spinor-helicity formalism to encode the data of massless fields of arbitrary spin on a cosmological horizon in de Sitter space. The evolution of free fields between past and future horizons (what might be called the free S-matrix in an observer’s causal patch) reduces to a simple Fourier transform in terms of these variables. We show how this arises via twistor theory, by decomposing the horizon-to-horizon problem into a pair of (more symmetric) horizon-to-twistor problems.

(ii) Similar to the static BPS black hole in AdS4 higher-spin theory [2], we solve the linearized Fronsdal equations with a source, and find the linearized version of the Didenko–Vasiliev black hole in de Sitter space. This is also shown to correspond holographically to the bilocal formulation of the boundary CFT.

(iii) We investigate the decomposition of the boundary CFT partition function in terms of spherical modes in the spinor-helicity basis. Further, we observe a discrepancy between the higher-spin-algebraic calculation of the partition function and the result of a direct calculation in the boundary CFT [3]; however, no such discrepancy arises at the level of n-point correlators, even when accounting for contact corrections. This paradox suggests a failure of locality in higher-spin theory, even on the boundary. A way forward from here is to introduce spin-locality as a replacement for spacetime locality, echoing recent developments in the bulk theory.

[1] A. David, N. Fischer, and Y. Neiman. Spinor-helicity variables for cosmological horizons in de Sitter space. Phys. Rev. D, 100:045005 (2019).

[2] V. E. Didenko, and M. A. Vasiliev. Static BPS black hole in 4d higher-spin gauge theory. Phys. Lett. B, 682:3, 305–315 (2009).

[3] D. Anninos et al. Cosmological shapes of higher-spin gravity. Journal of Cosmology and Astroparticle Physics, 2019:4 (2019).

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