Symmetries of supergravity backgrounds and supersymmetric field theory

Kuzenko, Sergei M.; Raptakis, Emmanouil S. N.

doi:10.1007/jhep04(2020)133

Cited by 21 publications

(22 citation statements)

References 161 publications

(210 reference statements)

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“…We find that the relations (A.30) and (A.31) exactly reproduce the U(1) superspace super-Weyl transformations [14,16,65].…”

Section: A N = 1 Conformal Superspace In Four Dimensionsmentioning

confidence: 67%

“…2 This gauge transformation law was introduced in ref. [14] within the U(1) superspace approach [15,16].…”

Section: Jhep08(2020)068mentioning

confidence: 99%

“…However, if the skeleton is supplemented by the non-minimal primary correction 14) then the sum of the two sectors…”

Section: Jhep08(2020)068mentioning

confidence: 99%

“…In this section we introduce the higher-spin generalisations of the conformal gravitino supermultiplet. These are described by the primary gauge prepotentials Υ α(n) , which were first introduced in U(1) superspace [14]. For a discussion of the models described by the prepotentials Υ α(n)α(m) , with n ≥ m > 0, we refer the reader to [5,13] and appendix B.3.…”

Section: Jhep08(2020)068mentioning

confidence: 99%

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New locally (super)conformal gauge models in Bach-flat backgrounds

Kuzenko

Ponds

Raptakis

2020

J. High Energ. Phys.

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For every conformal gauge field h α(n)α(m) in four dimensions, with n ≥ m > 0, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the Weyl tensor is non-vanishing, however, gauge invariance holds for a pure conformal field in the following cases: (i) n = m = 1 (Maxwell's field) on arbitrary gravitational backgrounds; and (ii) n = m + 1 = 2 (conformal gravitino) and n = m = 2 (conformal graviton) on Bach-flat backgrounds. It is believed that in other cases certain lower-spin fields must be introduced to ensure gauge invariance in Bach-flat backgrounds, although no closedform model has yet been constructed (except for conformal maximal depth fields with spin s = 5/2 and s = 3). In this paper we derive such a gauge-invariant model describing the dynamics of a conformal gauge field h α(3)α coupled to a self-dual two-form. Similar to other conformal higher-spin theories, it can be embedded in an off-shell superconformal gaugeinvariant action. To this end, we introduce a new family of N = 1 superconformal gauge multiplets described by unconstrained prepotentials Υ α(n) , with n > 0, and propose the corresponding gauge-invariant actions on conformally-flat backgrounds. We demonstrate that the n = 2 model, which contains h α(3)α at the component level, can be lifted to a Bach-flat background provided Υ α(2) is coupled to a chiral spinor Ω α. We also propose families of (super)conformal higher-derivative non-gauge actions and new superconformal operators in any curved space. Finally, through considerations based on supersymmetry, we argue that the conformal spin-3 field should always be accompanied by a conformal spin-2 field in order to ensure gauge invariance in a Bach-flat background.

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“…We find that the relations (A.30) and (A.31) exactly reproduce the U(1) superspace super-Weyl transformations [14,16,65].…”

Section: A N = 1 Conformal Superspace In Four Dimensionsmentioning

confidence: 67%

“…2 This gauge transformation law was introduced in ref. [14] within the U(1) superspace approach [15,16].…”

Section: Jhep08(2020)068mentioning

confidence: 99%

“…However, if the skeleton is supplemented by the non-minimal primary correction 14) then the sum of the two sectors…”

Section: Jhep08(2020)068mentioning

confidence: 99%

Section: Jhep08(2020)068mentioning

confidence: 99%

See 2 more Smart Citations

New locally (super)conformal gauge models in Bach-flat backgrounds

Kuzenko

Ponds

Raptakis

2020

J. High Energ. Phys.

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“…In the supersymmetric case, however, the program of studying the higher symmetries of the so-called super-Laplacians and related geometric structures in diverse dimensions has been initiated only a few years ago [72][73][74], mostly in Minkowski superspace (M d|δ N , D). So far there has been only one publication [75] devoted to the higher symmetries of supersymmetric wave equations in curved supergravity backgrounds. The present paper is aimed, in part, at a study of the higher symmetries of several on-shell supermultiplets in a background of N = (1, 0) conformal supergravity in six dimensions.…”

Section: Jhep03(2021)157mentioning

confidence: 99%

Symmetries of $$ \mathcal{N} $$ = (1, 0) supergravity backgrounds in six dimensions

Kuzenko

Lindström

Raptakis

et al. 2021

J. High Energ. Phys.

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General $$ \mathcal{N} $$ N = (1, 0) supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) SU(2) superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield ϵα, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector ξa and tensor ζa(n) superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d’Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on a limited class of backgrounds, including all conformally flat ones.

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Three‐Point Functions of Higher‐Spin Supercurrents in 4D N=1${{\cal N}}=1$ Superconformal Field Theory

Buchbinder

Hutomo

Tartaglino‐Mazzucchelli

2022

Fortschritte der Physik

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We develop a general formalism to study the three‐point correlation functions of conserved higher‐spin supercurrent multiplets Jαfalse(rfalse)α̇false(rfalse)$J_{\alpha (r) \dot{\alpha }(r)}$ in 4D scriptN=1${\cal N}=1$ superconformal theory. All the constraints imposed by scriptN=1${\cal N}=1$ superconformal symmetry on the three‐point function false⟨Jα(r1)trueα̇(r1)Jβ(r2)trueβ̇(r2)Jγ(r3)trueγ̇(r3)false⟩$\langle J_{\alpha (r_1) \dot{\alpha }(r_1)} J_{\beta (r_2) \dot{\beta }(r_2) }J_{\gamma (r_3) \dot{\gamma }(r_3)}\rangle$ are systematically derived for arbitrary r1,r2,r3$r_1, r_2, r_3$, thus reducing the problem mostly to computational and combinatorial. As an illustrative example, we explicitly work out the allowed tensor structures contained in false⟨Jα(r)trueα̇(r)Jβtrueβ̇Jγtrueγ̇false⟩$\langle J_{\alpha (r) \dot{\alpha }(r)} J_{\beta \dot{\beta } } J_{\gamma \dot{\gamma }}\rangle$, where Jαα̇$J_{\alpha \dot{\alpha }}$ is the supercurrent. We find that this three‐point function depends on two independent tensor structures, though the precise form of the correlator depends on whether r is even or odd. The case r=1$r=1$ reproduces the three‐point function of the ordinary supercurrent derived by Osborn. Additionally, we present the most general structure of mixed correlators of the form false⟨LLJα(r)trueα̇(r)false⟩$\langle L L J_{\alpha (r) \dot{\alpha }(r)}\rangle$ and false⟨Jα(r1)trueα̇(r1)Jβ(r2)trueβ̇(r2)Lfalse⟩$\langle J_{\alpha (r_1) \dot{\alpha }(r_1)} J_{\beta (r_2) \dot{\beta }(r_2)} L \rangle$, where L is the flavour current multiplet.

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Symmetries of supergravity backgrounds and supersymmetric field theory

Cited by 21 publications

References 161 publications

New locally (super)conformal gauge models in Bach-flat backgrounds

New locally (super)conformal gauge models in Bach-flat backgrounds

Symmetries of $$ \mathcal{N} $$ = (1, 0) supergravity backgrounds in six dimensions

Three‐Point Functions of Higher‐Spin Supercurrents in 4D N=1${{\cal N}}=1$ Superconformal Field Theory

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