Operator algebra of free conformal currents via twistors

Gelfond, O. A.; Vasiliev, M. A.

doi:10.1016/j.nuclphysb.2013.09.001

Cited by 64 publications

(150 citation statements)

References 55 publications

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“…a Hilbert space, while the black hole sector is real vector space with positive definite bilinear form. The correspondence between star product algebras and free conformal fields [19,115,117] suggests that the Z 2 symmetry between the modules embedded into the oscillator algebra has a holographic counterpart, whereby the free conformal field theory at the boundary of anti-de Sitter spacetime, with its Hilbert space structure, can be mapped by a Z 2 transformation to another theory that we propose to associate to the black holes (or, rather, to the black-hole microstates, as discussed in the Introduction), with its Euclidean structure.…”

Section: Jhep10(2017)130mentioning

confidence: 99%

4D higher spin black holes with nonlinear scalar fluctuations

Iazeolla

Sundell

2017

J. High Energ. Phys.

216

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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.

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Section: Jhep10(2017)130mentioning

confidence: 99%

4D higher spin black holes with nonlinear scalar fluctuations

Iazeolla

Sundell

2017

J. High Energ. Phys.

216

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“…Abusing this terminology to the other Lie algebras, let us consider HS algebra associated with a Lie algebra g: 38) where U(g) and J (g) are respectively the UEA and Joseph ideal of g. As a vector space, hs(g) corresponds to the space of polynomials in elements of O min (g): 39) with…”

Section: Hs Algebras and Reductive Dual Pairsmentioning

confidence: 99%

Notes on higher-spin algebras: minimal representations and structure constants

Joung

Mkrtchyan

2014

J. High Energ. Phys.

148

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The higher-spin (HS) algebras relevant to Vasiliev's equations in various dimensions can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebra and consider the corresponding HS algebras. For sp 2N and so N , the minimal representations are unique so we get unique HS algebras. For sl N , the minimal representation has one-parameter family, so does the corresponding HS algebra. The so N HS algebra is what underlies the Vasiliev theory while the sl 2 one coincides with the 3D HS algebra hs [λ]. Finally, we derive the explicit expression of the structure constant of these algebras -more precisely, their bilinear and trilinear forms. Several consistency checks are carried out for our results.

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“…This UV fixed point in d = 5, which should correspond to Vasiliev's theory in AdS 6 with the ∆ = 2 scalar boundary condition, will be discussed in Section 4.3. a projection of the type A/B theory to the minimal theory containing even spins only, which has been conjectured to be dual to the O(N ) singlet sector of the theory of N real massless scalars/fermions. At the level of the 3-point functions these conjectures have been checked at leading order in N [27][28][29][30][31][32][33][34][35]. The Vasiliev theory in general dimensions [23], whose spectrum is dual to that of the U (N ) or O(N ) singlet sector of d-dimensional scalar CFT, is a generalization of the type A model in AdS 4 .…”

Section: Introductionmentioning

confidence: 99%

Higher spinAdSd+1/CFTdat one loop

2014

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Following [1], we carry out one loop tests of higher spin AdS d+1 /CFT d correspondences for d ≥ 2. The Vasiliev theories in AdS d+1 , which contain each integer spin once, are related to the U (N ) singlet sector of the d-dimensional CFT of N free complex scalar fields; the minimal theories containing each even spin once -to the O(N ) singlet sector of the CFT of N free real scalar fields. Using analytic continuation of higher spin zeta functions, which naturally regulate the spin sums, we calculate one loop vacuum energies in Euclidean AdS d+1 . In even d we compare the result with the O(N 0 ) correction to the a-coefficient of the Weyl anomaly; in odd d -with the O(N 0 ) correction to the free energy F on the d-dimensional sphere. For the theories of integer spins, the correction vanishes in agreement with the CFT of N free complex scalars. For the minimal theories, the correction always equals the contribution of one real conformal scalar field in d dimensions. As explained in [1], this result may agree with the O(N ) singlet sector of the theory of N real scalar fields, provided the coupling constant in the higher spin theory is identified as G N ∼ 1/(N −1). Our calculations in even d are closely related to finding the regularized a-anomalies of conformal higher spin theories. In each even d we identify two such theories with vanishing a-anomaly: a theory of all integer spins, and a theory of all even spins coupled to a complex conformal scalar. We also discuss an interacting UV fixed point in d = 5 obtained from the free scalar theory via an irrelevant double-trace quartic interaction. This interacting large N theory is dual to the Vasiliev theory in AdS 6 where the bulk scalar is quantized with the alternate boundary condition.

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Operator algebra of free conformal currents via twistors

Cited by 64 publications

References 55 publications

4D higher spin black holes with nonlinear scalar fluctuations

4D higher spin black holes with nonlinear scalar fluctuations

Notes on higher-spin algebras: minimal representations and structure constants

Higher spinAdSd+1/CFTdat one loop

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