Higher spin AdS${}_3$ gravity and Tits-Satake diagrams

Abstract

We investigate higher spin AdS${}_3$ gravity with real split forms of complex A${}_N$ B${}_N$, C${}_N$ and D${}_N$ Lie algebras. This is done by linking $SO(1,2)$ spin multiplets with splitted root systems using Tits-Satake diagrams of real forms. Unlike $SL(N,R)$, we show that the orthogonal families have two different higher spin (HS) spectrums: vectorial and spinorial. We find amongst others that the spinorial spectrum has an isolated spin j${}_{\mathcal{N}}$ given by $\mathcal{N}\left(\mathcal{N}+1\right)/2$ for $SO(\mathcal{N},1+\mathcal{N})$ and $\mathcal{N}\left(\mathcal{N}-1\right)/2$ for $SO(\mathcal{N},\mathcal{N})$. We implement these results into the computation of the HS partition functions in these gravity theories and identify the individual contributions of the higher spin fields; valuable to manoeuver the HS-BTZ black hole partition function

References in corpus (40)

• Quantum Gravity Partition Functions in Three Dimensions
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• One-loop Partition Functions of 3D Gravity
• Higher Spin Black Holes
• What We Don't Know about BTZ Black Hole Entropy
• New Boundary Conditions for AdS3
• Soft Heisenberg hair on black holes in three dimensions
• Spacelike Singularities and Hidden Symmetries of Gravity
• Enhanced asymptotic symmetry algebra of AdS3
• Towards metric-like higher-spin gauge theories in three dimensions
• Higher spin black hole entropy in three dimensions
• An sl(2, R) current algebra from AdS_3 gravity
• Higher Spin Theories in AdS_3 and a Gravitational Exclusion Principle
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• N=2 Supersymmetric Black Attractors in Six and Seven Dimensions
• Constraints on Higher Spin CFT${}_2$
• RG Cascades in Hyperbolic Quiver Gauge Theories
• A (0,2) Mirror Map
• Entropy of Pairs of Dual Attractors in 6D/7D
• D-string fluid in conifold: I. Topological gauge model
• On Black Hole Effective Potential in 6D/7D N=2 Supergravity
• New boundary conditions for (extended) ${\mathrm{AdS}}_3$ supergravity
• D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}
• 't Hooft lines of ADE-type and Topological Quivers
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• On the Spectrum of Pure Higher Spin Gravity
• Computing the Scalar Field Couplings in 6D Supergravity
• Extremal Higher Spin Black Holes
• Exploring new Boundary Conditions for $\mathcal{N}=(1,1)$ Extended Higher Spin $Ad{S}_3$ Supergravity
• The Schwarzian sector of higher spin CFTs
• Refining the Shifted Topological Vertex
• Towards a classification of branes in theories with eight supercharges
• Non Trivial Extension of the (1+2)-Poincaré Algebra and Conformal Invariance on the Boundary of $Ad{S}_3$
• $\mathcal{N}=(2,2)$ extended $\mathfrak{sl}(3|2)$ Chern-Simons $Ad{S}_3$ supergravity with new boundaries
• Lax Operator and superspin chains from 4D CS gauge theory
• Topological String on Toric CY3s in Large Complex Structure Limit
• Extremal Black Attractors in 8D Maximal Supergravity
• On Black Attractors in 8D and Heterotic/Type IIA Duality

Cited by in corpus (11)

• Finiteness of 3D higher spin gravity Landscape
• Black Flowers and Real Forms of Higher Spin Symmetries
• Fluctuating Ensemble Averages and the BTZ Threshold
• Black hole solutions of three dimensional E${}_6$-gravity
• Higher spin swampland conjecture for massive AdS${}_3$ gravity
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Topological 4D gravity and gravitational defects
• Landscape of Narain CFTs
• Algebraic Realisation of the Zamolodchikov Metric in Narain Theories
• Algebraic constructions of code lattices in Narain conformal field theories
• Code CFTs and Topological Matter