Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields

In this paper we continue and improve the analysis of the effective actions obtained by integrating out a scalar and a fermion field coupled to external symmetric sources, started in the previous paper. The first subject we study is the geometrization of the results obtained there, that is we express them in terms of covariant Jacobi tensors. The second subject concerns the treatment of tadpoles and seagull terms in order to implement off-shell covariance in the initial model. The last and by far largest part of the paper is a repository of results concerning all two point correlators (including mixed ones) of symmetric currents of any spin up to 5 and in any dimensions between 3 and 6. In the massless case we also provide formulas for any spin in any dimension.

“…Other papers of ours, related to the present one are, beside [1,42,43]. For future developments we think that important references are [44][45][46][47].…”

Section: Jhep01(2018)080mentioning

confidence: 67%

One-loop effective actions and higher spins. Part II

Bonora¹,

Cvitan²,

Prester³

et al. 2018

“…As for the section components, it is assumed that they have finite integrals over B in order to yield finite star products and traces; thus they should belong to L 1 (B). 10 As for connection components, it is instead assumed that they give rise to well-defined open Wilson lines, which can be implemented in noncommutative geometry using deformed oscillator algebras; for example, see [104][105][106].…”

Section: Jhep10(2017)130mentioning

confidence: 99%

“…We plan to assess how large the gauge transformation H is, i.e., how far the L-and Vasiliev gauge are from each other, by examining its effect on observables. As a first step, it is natural to examine zero-form charges, that is, decorated open Wilson lines in Z [106], which are known to contain higher spin amplitudes in their leading order.…”

Section: Jhep10(2017)130mentioning

confidence: 99%

4D higher spin black holes with nonlinear scalar fluctuations

Iazeolla

Sundell

2017

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.

“…In [38,45], it has been proposed that the extensive variables are the zero-form charges [14,37], and in [46] it has been proposed that a complete set of classical observables in the case that X4 has trivial topology is given by the space of twisted open Wilson lines in Z4. According to these proposals, the rigid symmetries of the vacuum should leave the extensive variables invariant while acting nontrivially on the microscopic variables; for related remarks, see [18,46]. 10 The full field configurations are thus assumed to contain contain asymptotically (anti-)de Sitter regions where the full tensor gauge fields φ a(s) approach Fronsdal fields give on shell in terms of polarization tensors that are non-linear functionals of the zero-form initial data C.…”

Section: Gauge Functionsmentioning

confidence: 99%

FRW and domain walls in higher spin gravity

Aros

Iazeolla

Noreña

et al. 2018

We present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in spacetime, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in (A)dS 4 . We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.