Conformal supergravity in three dimensions: off-shell actions

Butter, Daniel; Kuzenko, Sergei M.; Novak, Joseph D.; Tartaglino‐Mazzucchelli, Gabriele

doi:10.1007/jhep10(2013)073

Cited by 57 publications

(142 citation statements)

References 60 publications

(221 reference statements)

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“…In particular, the constraints for R(S) µν ip and R(K) µν a are identically satisfied for the composite gauge fields in (3.6). These results are generally in agreement with earlier off-shell results [15,16,[18][19][20] as well as with on-shell results [23,24].…”

Section: Jhep01(2016)156supporting

confidence: 92%

“…We emphasize that the results we are about to describe are consistent with results previously reported in the literature, such as in [15][16][17][18]. In particular they fully reproduce the non-linear results that were obtained in [19,20].…”

Section: N = 4 Conformal Supergravity In Three Dimensionssupporting

confidence: 91%

“…1 Some of the final results of the dimensional reduction procedure can be compared to existing results in the literature on N = 4 (conformal) supergravity theories in three dimensions (see e.g. [15][16][17][18][19][20] where further references can be found). We will discuss the details in due course.…”

Section: Jhep01(2016)156mentioning

confidence: 99%

“…The gravitini, and the spinor χ comprise 4 and 4 fermionic degrees of freedom, respectively. The covariant fields are described by a real scalar superfield of Weyl weight w = 1, subject to the constraint that the second-order superspace derivative D α i p D αj q is proportional to the trace with respect to the SO(4) indices [18,20]. Furthermore the transformation (3.3) can be understood as a parity transformation in the internal euclidean four-space parametrized by coordinates X I ∼ X i p .…”

Section: Jhep01(2016)156mentioning

confidence: 99%

“…Upon dimensional reduction the supersymmetry transformation rules (4.18) can be cast in the form, 20) where all fermionic terms were taken into account and where D µ denotes the supercovariant derivative in three dimensions. Again we suppressed the field-dependent SU(2) and Ssupersymmetry transformations.…”

Section: Jhep01(2016)156mentioning

confidence: 99%

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The off-shell c-map

Banerjee

Wit

Katmadas

2016

J. High Energ. Phys.

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Abstract:The off-shell version of the c-map is presented, based on a systematic offshell reduction from four to three space-time dimensions for supergravity theories with eight supercharges. In the reduction, the R-symmetry group is enhanced to local [SU(2) × SU(2)]/Z 2 ∼ = SO(4) and the c-map is effected by a parity transformation in the internal space that interchanges the two SU(2) factors. Vector and tensor supermultiplets are each others conjugate under the c-map and both can be dualized in three dimensions to (on-shell) hypermultiplets.As shown in this paper the off-shell formulation indeed leads to a clarification of many of the intricate issues that play a role in the c-map. The results for off-shell Lagrangians quadratic in space-time derivatives are analyzed in detail and compared to the literature. The underlying reasons are identified why not all of the four-dimensional tensor multiplet Lagrangians can be in the image of the c-map. The advantage of the off-shell approach is, that it also enables a systematic analysis of theories with higher-derivative couplings. This is demonstrated for a particular subclass of such theories, which, under certain conditions, are consistent under the c-map. In principle, explicit results for realistic four-dimensional type-II string compactifications can be explored in this way.

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Section: Jhep01(2016)156supporting

confidence: 92%

Section: N = 4 Conformal Supergravity In Three Dimensionssupporting

confidence: 91%

Section: Jhep01(2016)156mentioning

confidence: 99%

Section: Jhep01(2016)156mentioning

confidence: 99%

Section: Jhep01(2016)156mentioning

confidence: 99%

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The off-shell c-map

Banerjee

Wit

Katmadas

2016

J. High Energ. Phys.

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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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Covariant Superspace Approaches to $$\mathscr {N}=\text{2}$$ Supergravity

Kuzenko,

Raptakis,

Tartaglino-Mazzucchelli

2023

Handbook of Quantum Gravity

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We develop a superspace formulation for N = 3 conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group SU(2, 2|3). Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives) is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor W α of dimension +1/2 and its conjugate. Associated with W α is its primary descendant B i j of dimension +2, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for N = 3 conformal supergravity. We describe the model for linearised N = 3 conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses U(1) duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the U(3) superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called SU(3) superspace, which can also be used to describe N = 3 conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell N = 3 super Yang-Mills theory coupled to conformal supergravity.

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Conformal supergravity in three dimensions: off-shell actions

Cited by 57 publications

References 60 publications

The off-shell c-map

The off-shell c-map

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

Covariant Superspace Approaches to $$\mathscr {N}=\text{2}$$ Supergravity

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