Chern-Simons matter theories and higher spin gravity

Properties of the resolution operator d * loc in higher-spin equations, that leads to local current interactions at the cubic order and minimally nonlocal higher-order corrections, are formulated in terms of the condition on the class of master fields of higher-spin theory that restricts both the dependence on the spinor Y , Z variables and on the contractions of indices between the constituent fields in bilinear terms. The Green function in the sector of zero-forms is found for the case of constituent fields carrying helicities of opposite signs. It is shown that the local resolution d * loc differs from the conventional De Rham resolution d * Z by a non-local shift.

Section: Jhep01(2018)062mentioning

confidence: 79%

On the local frame in nonlinear higher-spin equations

Vasiliev

2018

“…We compare the result (3.16) with the prediction (2.18) of duality for the Higgsed phase 10 In [1], the free energy vCB[ρB] depended on m cri B which was a parameter in the theory. After the replacement (3.14), the dependence on the parameter m cri B is replaced by a dependence on the field V (x).…”

Section: An Effective Action For the Higgs Field Vmentioning

confidence: 93%

Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories

Dey

Halder

Jain

et al. 2018

It has been conjectured that Chern-Simons (CS) gauged 'regular' bosons in the fundamental representation are 'level-rank' dual to CS gauged critical fermions also in the fundamental representation. Generic relevant deformations of these conformal field theories lead to one of two distinct massive phases. In previous work, the large N thermal free energy for the bosonic theory in the unHiggsed phase has been demonstrated to match the corresponding fermionic results under duality. In this note we evaluate the large N thermal free energy of the bosonic theory in the Higgsed phase and demonstrate that our results, again, perfectly match the predictions of duality. Our computation is performed in a unitary gauge by integrating out the physical excitations of the theory -i.e. W bosonsat all orders in the 't Hooft coupling. Our results allow us to construct an exact quantum effective potential forφφ, the lightest gauge invariant scalar operator in the theory. In the zero temperature limit this exact Landau-Ginzburg potential is non-analytic atφφ = 0. The extrema of this effective potential at positiveφφ solve the gap equations in the Higgsed phase while the extrema at negativeφφ solve the gap equations in the unHiggsed phase. Our effective potential is bounded from below only for a certain range of x 6 (the parameter that governs sextic interactions of φ). This observation suggests that the regular boson theory has a stable vacuum only when x 6 lies in this range. 1 anshuman@theory.tifr.res.in 2 indranil.halder@tifr.res.in 3 sachin.jain@iiserpune.ac.in 4 lavneet@theory.tifr.res.in 5 minwalla@theory.tifr.res.in 6 naveensp@theory.tifr.res.in A Previously known results for the large N free energy 32 A.1 Results for the critical fermion theory 33 A.2 Results for regular bosons in the unHiggsed Phase 35 A.3 Duality in the unHiggsed phase and a prediction for the Higgsed phase 36 A.3.1 unHiggsed phase: sgn(X F ) = −sgn(λ B ) 37 A.3.2 Higgsed phase: sgn(X F ) = sgn(λ B ) 37 B The tadpole from W boson loops 38 C The critical boson scaling limit 41 -1 -

“…The former path, whereby the internal degrees of freedom of Vasiliev's integrable system are viewed essentially as auxiliary fields, without any proper dynamics of their own, involves a reduction down to a set of deformed Fronsdal equations on the spacetime submanifold [4, 7-9, 13, 30, 84, 92-95], to be directly compared with those of the quasi-local deforrmed Fronsdal theory. Although this procedure introduces ambiguities concerning the embedding of spacetime into the full noncommutative geometry and the internal gauge fixing, one may entertain the idea that the quasi-locality requirement provides a guiding principle; for recent progress, see [95][96][97].…”

Section: Motivationsmentioning

confidence: 99%

“…The origin of the singularity in H (1) is intimately related to the holomorphic gauge we start from, in which the two-form curvature has a δ-function source in twistor space. It is expected that, extending Vasiliev's gauge to higher orders, H induce a redefinition of the initial data for the zero-form and for the spacetime one-form, to be compared with those recently proposed by Vasiliev in order to rewrite the non-linearities encoded in the equations in terms of current interactions [95] (see also [96,97] for recent holographic tests of the local second-order interaction terms found in [95]). 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.…”

Section: Jhep10(2017)130mentioning

confidence: 99%

4D higher spin black holes with nonlinear scalar fluctuations

Iazeolla

Sundell

2017

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.