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<p>SYK models provide an interesting playground for exploring the <i>AdS</i><sub>2</sub>/<i>CFT</i><sub>1</sub> correspondence. We focus on a class of SYK models that exhibit higher-spin symmetry, whose gravity sector is described by a BF theory generalizing Jackiw-Teitelboim gravity to higher spins. We further develop this framework by constructing consistent interactions between higher-spin gauge fields and scalar matter fields. Two concrete realizations are proposed: Model A, arising from a deformation of the universal enveloping algebra of <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="fraktur">sl</mi> <mfenced close=")" open="(" separators=","> <mn>2</mn> <mi>ℝ</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathfrak{sl}\left(2,\mathbb{R}\right) \)</EquationSource> </InlineEquation>, and Model B, a perturbatively local Poisson sigma-model with an infinite-dimensional target space. While both capture higher-spin dynamics on (<i>A</i>)<i>dS</i><sub>2</sub>, they differ in their algebraic structures and locality properties, thus offering complementary perspectives on higher-spin holography.</p>

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Higher-spin Poisson sigma models and holographic duality for SYK models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月9日

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  • Xavier Bekaert,
  • Alexey Sharapov,
  • Evgeny Skvortsov

摘要

SYK models provide an interesting playground for exploring the AdS2/CFT1 correspondence. We focus on a class of SYK models that exhibit higher-spin symmetry, whose gravity sector is described by a BF theory generalizing Jackiw-Teitelboim gravity to higher spins. We further develop this framework by constructing consistent interactions between higher-spin gauge fields and scalar matter fields. Two concrete realizations are proposed: Model A, arising from a deformation of the universal enveloping algebra of sl 2 ℝ \( \mathfrak{sl}\left(2,\mathbb{R}\right) \) , and Model B, a perturbatively local Poisson sigma-model with an infinite-dimensional target space. While both capture higher-spin dynamics on (A)dS2, they differ in their algebraic structures and locality properties, thus offering complementary perspectives on higher-spin holography.