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Covariant superspace approaches to ${\cal N}=2$ supergravity

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arxiv 2211.11162 v2 pith:62ZRFILT submitted 2022-11-21 hep-th gr-qcmath-phmath.MP

S. M. Kuzenko , E. S. N. Raptakis , G. Tartaglino-Mazzucchelli This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP
keywords superspaceconformalcovariantsupergravityapproachesinvariantsmathsfstructure
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abstract

We provide a unified description of the three covariant superspace approaches to ${\cal N}=2$ conformal supergravity in four dimensions: (i) conformal superspace; (ii) $\mathsf{U}(2)$ superspace; and (iii) $\mathsf{SU}(2)$ superspace. Each of them can be used to formulate general supergravity-matter systems, although conformal superspace has the largest structure group and is intimately related to the superconformal tensor calculus. We review the structure of covariant projective multiplets and demonstrate how they are used to describe pure and matter-coupled supergravity, including locally superconformal off-shell sigma models. Higher-derivative invariants, topological invariants and super-Weyl anomalies are also briefly discussed.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Six-dimensional $\mathcal{N}=(2,0)$ Conformal Superspace

    hep-th 2025-06 conditional novelty 8.0 of 10

    A new off-shell 6D N=(2,0) conformal superspace is constructed, and its unique Bach tensor superfield is derived up to overall scaling.

  2. Superform Approach to Equivariant Localization in Supergravity

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Closed superforms in superspace generate equivariantly closed polyforms for localization in off-shell 4d N=2 conformal supergravity, applied to vector, linear, chiral, and BF multiplets.

  3. Nonlinear self-duality for arbitrary spin, superspin, and supersymmetry type

    hep-th 2026-02 conditional novelty 4.0 of 10

    Every U(1) duality-invariant (super)conformal gauge theory of arbitrary (super)spin obeys a universal self-duality equation, is Legendre self-dual, and (for spin > 1) lives only on conformally flat backgrounds.

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