Type-B formal higher spin gravity

Grigoriev, Maxim; Skvortsov, Evgeny

doi:10.1007/jhep05(2018)138

Cited by 28 publications

(32 citation statements)

References 96 publications

(231 reference statements)

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“…The body of the zero locus of Q P is the stationary surface and indeed we get conditions w a| − v |a = 0 and v [a|b] = 0 in accord with (51). The explicit form of the complete Q P simplifies if one uses coordinates ψ α a 1 ...a l |b 1 ...b k that coincide with u α a 1 ...a l |b 1 ...b k at θ = 0 and satisfy D θ a ψ α a 1 ...a l |b 1 ...b k = 0.…”

Section: Appendix: Super Jet-bundlesupporting

confidence: 55%

“…Further examples are gauge theories of boundary values in the context of the AdS/CFT correspondence, which immediately arise in BV form if one starts from the BV formulation in the bulk. [48][49][50][51] Defining a theory in BV terms from the outset naturally leads to a more general class of systems than one would arrive by applying BV procedure to a given theory defined in terms of a Lagrangian or equations of motion. This motivates introducing a notion of gauge PDE as a system defined from the very beginning in terms of BV-BRST differential.…”

Section: Introductionmentioning

confidence: 99%

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Gauge PDE and AKSZ‐type Sigma Models

Grigoriev

Kotov

2019

Fortschritte der Physik

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A gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV‐BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular attention to globally well‐defined definitions and equivalences of such objects. We demonstrate that a natural geometrical language to work with gauge PDEs is that of Q‐bundles. In particular, we demonstrate that any gauge PDE can be embedded into a super‐jet bundle of the Q‐bundle. This gives a globally well‐defined version of the so‐called parent formulation. In the case of reparameterization‐invariant systems, the parent formulation takes the form of an AKSZ‐type sigma model with an infinite‐dimensional target space.

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Section: Appendix: Super Jet-bundlesupporting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Gauge PDE and AKSZ‐type Sigma Models

Grigoriev

Kotov

2019

Fortschritte der Physik

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“…2.4. To summarize, higher spin fields can consistently propagate on higher spin flat backgrounds [14,29,49]. This result illustrates the physical meaning of the, otherwise quite abstract, Hochschild two-cocycle.…”

Section: )mentioning

confidence: 56%

“…In this regard it is worth mentioning that the Type-A,B theories of [29,49] seem to have nothing to do with the deformed oscillators and are based on some other resolution of the Hochschild complex. Below we briefly discuss another realization of the Type-B theory.…”

Section: )mentioning

confidence: 99%

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Formal Higher Spin Gravities

Sharapov

Skvortsov

2019

Nuclear Physics B

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We present a complete solution to the problem of Formal Higher Spin Gravitiesformally consistent field equations that gauge a given higher spin algebra and describe free higher spin fields upon linearization. The problem is shown to be equivalent to constructing a certain deformation of the higher spin algebra as an associative algebra.Given this deformation, all interaction vertices are explicitly constructed. All formal solutions of the equations are explicitly described in terms of an auxiliary Lax pair, the deformation parameter playing the role of the spectral one. We also discuss a natural set of observables associated to such theories, including the holographic correlation functions. As an application, we give another form of the Type-B formal Higher Spin Gravity and discuss a number of systems in five dimensions.

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Conformal Interactions Between Matter and Higher‐Spin (Super)Fields

Kuzenko

Ponds

Raptakis

2022

Fortschritte der Physik

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In even spacetime dimensions, the interacting bosonic conformal higher‐spin (CHS) theory can be realised as an induced action. The main ingredient in this definition is the model scriptSfalse[φ,hfalse]$\mathcal {S}[\varphi ,h]$ describing a complex scalar field φ coupled to an infinite set of background CHS fields h, with scriptSfalse[φ,hfalse]$\mathcal {S}[\varphi ,h]$ possessing a non‐abelian gauge symmetry. Two characteristic features of the perturbative constructions of scriptSfalse[φ,hfalse]$\mathcal {S}[\varphi , h]$ given in the literature are: (i) the background spacetime is flat; and (ii) conformal invariance is not manifest. In the present paper we provide a new derivation of this action in four dimensions such that (i) scriptSfalse[φ,hfalse]$\mathcal {S}[\varphi , h]$ is defined on an arbitrary conformally‐flat background; and (ii) the background conformal symmetry is manifestly realised. Next, our results are extended to the scriptN=1$\mathcal {N}=1$ supersymmetric case. Specifically, we construct, for the first time, a model scriptSfalse[normalΦ,Hfalse]$\mathcal {S}[\Phi , H]$ for a conformal scalar/chiral multiplet Φ coupled to an infinite set of background higher‐spin superfields H. Our action possesses a non‐abelian gauge symmetry which naturally generalises the linearised gauge transformations of conformal half‐integer superspin multiplets. The other fundamental features of this model are: (i) scriptSfalse[normalΦ,Hfalse]$\mathcal {S}[\Phi , H]$ is defined on an arbitrary conformally‐flat superspace background; and (ii) the background scriptN=1$\mathcal {N}=1$ superconformal symmetry is manifest. Making use of scriptSfalse[normalΦ,Hfalse]$\mathcal {S}[\Phi , H]$, an interacting superconformal higher‐spin theory can be defined as an induced action.

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Type-B formal higher spin gravity

Cited by 28 publications

References 96 publications

Gauge PDE and AKSZ‐type Sigma Models

Gauge PDE and AKSZ‐type Sigma Models

Formal Higher Spin Gravities

Conformal Interactions Between Matter and Higher‐Spin (Super)Fields

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