On classical solutions of 4d supersymmetric higher spin theory

Bourdier, Jun; Drukker, Nadav

doi:10.1007/jhep04(2015)097

Cited by 13 publications

(20 citation statements)

References 39 publications

(153 reference statements)

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“…It is worth mentioning that even by working without the gauge function method, with a specific choice of gauge the Didenko-Vasiliev solution can be simplified in such a way that the W connection is reduced to the vacuum one W 0 . This simplification was studied in [44], along with the embedding of the solution in the N = 2 and N = 4 supersymmetric extensions of the bosonic Vasiliev equations.…”

Section: Direct Methods and The Didenko-vasiliev Solutionmentioning

confidence: 99%

On Exact Solutions and Perturbative Schemes in Higher Spin Theory

2018

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Abstract:We review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev's equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with the symmetries of a domain wall is also described. Furthermore, we review two proposed perturbative schemes: one based on perturbative treatment of the twistor space field equations followed by inverting Fronsdal kinetic terms using standard Green's functions; and an alternative scheme based on solving the twistor space field equations exactly followed by introducing the spacetime dependence using perturbatively defined gauge functions. Motivated by the need to provide a higher spin invariant characterization of the exact solutions, aspects of a proposal for a geometric description of Vasiliev's equation involving an infinite dimensional generalization of anti de Sitter space are revisited and improved.

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Section: Direct Methods and The Didenko-vasiliev Solutionmentioning

confidence: 99%

On Exact Solutions and Perturbative Schemes in Higher Spin Theory

2018

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“…The BH solutions of [14][15][16] need further investigation to clarify whether they belong to the proper class of functions. A closely related problem is that the solution of [14] was obtained in a nonstandard gauge that complicates its physical interpretation.…”

Section: Resultsmentioning

confidence: 99%

Star-product functions in higher-spin theory and locality

Vasiliev

2015

J. High Energ. Phys.

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Properties of the functional classes of star-product elements associated with higher-spin gauge fields and gauge parameters are elaborated. Cohomological interpretation of the nonlinear higher-spin equations is given. An algebra H, where solutions of the nonlinear higher-spin equations are valued, is found. A conjecture on the classes of starproduct functions underlying (non)local maps and gauge transformations in the nonlinear higher-spin theory is proposed.

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“…This closed manifold can be taken to be the boundary of an AKSZ bulk manifold in one higher dimension, to which suitable TVO's can be attached. The resulting quantum field theory provides a functorial map from the 12 Several interesting questions can be addressed directly within an AKSZ-inspired semi-classical treatment of pure gravity; for example, the Gibbons-Hawking entropy can be interpreted as being due to geometrical entanglement involving de Sitter vacua with boundaries and defects representing static observers [19].…”

Section: Horizontal Forms and Quasi-topological Noncommutative Field mentioning

confidence: 99%

“…For the literature on solutions of this type in four spacetime dimensions, see[5][6][7][8][9][10][11][12][13][14]; see also[15][16][17] for exact solutions in three spacetime dimensions, and[18] for solutions obtained in axial gauge in oscillator space.…”

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confidence: 99%

Higher spin fluctuations on spinless 4D BTZ black hole

Aros

Iazeolla

Sundell

et al. 2019

J. High Energ. Phys.

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We construct linearized solutions to Vasiliev's four-dimensional higher spin gravity on warped AdS 3 × ξ S 1 which is an Sp(2) × U (1) invariant non-rotating BTZ-like black hole with R 2 × T 2 topology. The background can be obtained from AdS 4 by means of identifications along a Killing boost K in the region where ξ 2 ≡ K 2 ⩾ 0, or, equivalently, by gluing together two Bañados-Gomberoff-Martinez eternal black holes along their past and future space-like singularities (where ξ vanishes) as to create a periodic (non-Killing) time. The fluctuations are constructed from gauge functions and initial data obtained by quantizing inverted harmonic oscillators providing an oscillator realization of K and of a commuting Killing boost K. The resulting solution space has two main branches in which K star commutes and anti-commutes, respectively, to Vasiliev's twistedcentral closed two-form J. Each branch decomposes further into two subsectors generated from ground states with zero momentum on S 1 . We examine the subsector in which K anti-commutes to J and the ground state is U (1) K × U (1) K -invariant of which U (1) K is broken by momenta on S 1 and U (1) K by quasi-normal modes. We show that a set of U (1) K -invariant modes (with n units of S 1 momenta) are singularity-free as master fields living on a total bundle space, although the individual Fronsdal fields have membrane-like singularities at K 2 = 1. We interpret our findings as an example where Vasiliev's theory completes singular classical Lorentzian geometries into smooth higher spin geometries.5 It is worth mentioning that, from the point of view of the standard spin-2 geometry, there is no four-dimensional uplift of the three-dimensional rotating BTZ black hole, since, differently from the spinless case, the presence of an extra spatial dimension erases the horizon [38]. Since one of the issues to be studied in this paper is the resolution of singularities of fluctuation fields at the horizon within Vasiliev's higher spin gravity, we shall choose to investigate the linearized dynamics around a vacuum solution corresponding to the four-dimensional (topologically extended) non-rotating BTZ-like black hole.6 Rather, in constructing unfolded systems of equations it is usually assumed that if the frame field is invertible then the system must admit a dual interpretation as a complex for an algebraic differential whose cohomology in different degrees consists of the dynamical Fronsdal fields, their gauge parameters, and equations of motion and Bianchi identities [41]; for analogous treatment of mixed symmetry fields, see [43,44].

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On classical solutions of 4d supersymmetric higher spin theory

Cited by 13 publications

References 39 publications

On Exact Solutions and Perturbative Schemes in Higher Spin Theory

On Exact Solutions and Perturbative Schemes in Higher Spin Theory

Star-product functions in higher-spin theory and locality

Higher spin fluctuations on spinless 4D BTZ black hole

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