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Chiral Higher Spin Gravity and Convex Geometry

by Alexey Sharapov, Evgeny Skvortsov, Richard Van Dongen

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Submission summary

Authors (as registered SciPost users): Evgeny Skvortsov
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-04-11
Date submitted: 2023-02-28 15:37
Submitted by: Skvortsov, Evgeny
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


Chiral Higher Spin Gravity is the minimal extension of the graviton with propagating massless higher spin fields. It admits any value of the cosmological constant, including zero. Its existence implies that Chern-Simons vector models have closed subsectors and supports the $3d$ bosonization duality. In this letter, we explicitly construct an $A_\infty$-algebra that determines all interaction vertices of the theory. The algebra turns out to be of pre-Calabi-Yau type. The corresponding products, some of which originate from Shoikhet-Tsygan-Kontsevich formality, are given by integrals over the configuration space of convex polygons.

Published as SciPost Phys. 14, 162 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-3-3 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2209.01796v2, delivered 2023-03-03, doi: 10.21468/SciPost.Report.6838


1 - interesting results
2 - well-motivated
3 - concise


The paper is:
1 - too concise to get a proper grasp of the technicalities
2 - just the short version of a (long) companion paper (arXiv:2209.15441) with complete technical details


The authors have taken my suggestions of changes into account and have answered the questions of the other referee, so I recommend the paper for publication in SciPost as it stands now.

  • validity: top
  • significance: high
  • originality: high
  • clarity: good
  • formatting: perfect
  • grammar: good

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Anonymous on 2023-03-03  [id 3429]

I recommend publication.