A minimal BV action for Vasiliev’s four-dimensional higher spin gravity

Self Cite

216

Abstract:We construct an infinite-dimensional space of solutions to Vasiliev's equations in four dimensions that are asymptotic to AdS spacetime and superpose massless scalar particle modes over static higher spin black holes. Each solution is obtained by a large gauge transformation of an all-order perturbatively defined particular solution given in a simple gauge, in which the spacetime connection vanishes, the twistor space connection is holomorphic, and all local degrees of freedom are encoded into the residual twistor space dependence of the spacetime zero-forms. The latter are expanded over two dual spaces of Fock space operators, corresponding to scalar particle and static black hole modes, equipped with positive definite sesquilinear and bilinear forms, respectively. Switching on an AdS vacuum gauge function, the twistor space connection becomes analytic at generic spacetime points, which makes it possible to reach Vasiliev's gauge, in which Fronsdal fields arise asymptotically, by another large transformation given here at first order. The particle and black hole modes are related by a twistor space Fourier transform, resulting in a black hole backreaction already at the second order of classical perturbation theory. We speculate on the existence of a fine-tuned branch of moduli space that is free from black hole modes and directly related to the quasi-local deformed Fronsdal theory. Finally, we comment on a possible interpretation of the higher spin black hole solutions as black-hole microstates.

Section: Jhep10(2017)130mentioning

confidence: 99%

“…Eliminating these terms perturbatively, using the constraint on Φ, yields a canonical Cartan curvature for W . 16 Under the parity operation P , one has P (φ) = φ in the type A model, and P (φ) = −φ in the type B model.…”

Section: Jhep10(2017)130mentioning

confidence: 99%

4D higher spin black holes with nonlinear scalar fluctuations

Iazeolla

Sundell

2017

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216

“…The tree-level free energy G −1 HS F (−1) HS is the saddle point action of the Vasiliev theory. Although there are some propositions on the actions of the Vasiliev theory [96][97][98][99], it is not obvious to compute the tree level free energy from these actions. Thus we focus on the leading correction F (0) HS , the one-loop free energy of the Vasiliev theory.…”

Section: Jhep08(2016)174mentioning

confidence: 99%

ABJ theory in the higher spin limit

Hirano

Honda

Shigemori

2016

Abstract:We study the conjecture made by Chang, Minwalla, Sharma, and Yin on the duality between the N = 6 Vasiliev higher spin theory on AdS 4 and the N = 6 Chern-Simons-matter theory, so-called ABJ theory, with gauge group U(N ) × U(N + M ). Building on our earlier results on the ABJ partition function, we develop the systematic 1/M expansion, corresponding to the weak coupling expansion in the higher spin theory, and compare the leading 1/M correction, with our proposed prescription, to the one-loop free energy of the N = 6 Vasiliev theory. We find an agreement between the two sides up to an ambiguity that appears in the bulk one-loop calculation.

“…We truncate the models further as follows: 27) where W ± and T ± are independent of Γ i and κ y , and…”

Section: Jhep05(2016)003mentioning

confidence: 99%

An action for matter coupled higher spin gravity in three dimensions

Bonezzi

Boulanger

Sezgin

et al. 2016

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We propose a covariant Hamiltonian action for the Prokushkin and Vasiliev's matter coupled higher spin gravity in three dimensions. The action is formulated on X 4 ×Z 2 where X 4 is an open manifold whose boundary contains spacetime and Z 2 is a noncommutative twistor space. We examine various consistent truncations to models of BF type in X 4 and Z 2 with B 2 terms and central elements. They are obtained by integrating out the matter fields in the presence of a vacuum expectation value ν ∈ R for the zero-form master field. For ν = 0, we obtain a model on X 4 containing Blencowe's action and a model on Z 2 containing the Prokushkin-Segal-Vasiliev action. For generic ν (including ν = 0), we propose an alternative model on X 4 with gauge fields in the Weyl algebra of Wigner's deformed oscillator algebra and Lagrange multipliers in the algebra of operators acting in the Fock representation space of the deformed oscillators.