Scalar field in an arbitrary dimension from the standpoint of higher-spin Gauge theory

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.

Section: Discussionmentioning

confidence: 99%

An action for matter coupled higher spin gravity in three dimensions

Bonezzi

Boulanger

Sezgin

et al. 2016

“…This condition provides a tool for the search of manifestly supersymmetric formulation of the theory. In this context, it should be noted that because the dynamical equations of an unfolded system are classified in terms of the so-called σ − -cohomology [21], this makes it possible to derive an off-shell unfolded system directly from the on-shell one by finding such a completion of the unfolded equations in which the corresponding sector of the σ − -cohomology vanishes. In principle, this provides a general approach for the search of manifestly supersymmetric versions of the theories in question.…”

Section: Jhep05(2014)140mentioning

confidence: 99%

“…Classification of dynamical fields, gauge symmetries and dynamical equations of the unfolded systems can be performed in terms of so-called σ − -cohomology [2,3,6,21]. Let a linear unfolded system be of the form …”

Section: σ − -Cohomologymentioning

confidence: 99%

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Off-shell scalar supermultiplet in the unfolded dynamics approach

Misuna

Vasiliev

2014

Self Cite

We show how manifestly supersymmetric action for Wess-Zumino model can be constructed within the unfolded dynamics approach. The off-shell unfolded system for N = 1, D = 4 scalar supermultiplet is found. The action is presented in the form of integral of a closed 4-form over any (4, 0) surface in superspace as well as a superspace integral of an integral form or a chiral integral form. The proposed method is argued to provide a most general tool for the analysis of manifestly supersymmetric functionals.

“…In the following we will mostly work with Fourier-transformed fields, 63) which leads to the Fourier-transformed expressions for J q…”

Section: Conservationmentioning

confidence: 99%

Higher spins and matter interacting in dimension three

Kessel

Gómez

Skvortsov

et al. 2015

105

The spectrum of Prokushkin-Vasiliev Theory is puzzling in light of the Gaberdiel-Gopakumar conjecture because it generically contains an additional sector besides higher-spin gauge and scalar fields. We find the unique truncation of the theory avoiding this problem to order 2 in perturbations around AdS 3 . The second-order backreaction on the physical gauge sector induced by the scalars is computed explicitly. The cubic action for the physical fields is determined completely. The subtle issue of the allowed class of pseudo-local field redefinitions is discussed.