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$\mathcal{N}=2$ superconformal gravitino in harmonic superspace

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arxiv 2412.14822 v2 pith:RCAFCDRG submitted 2024-12-19 hep-th

classification hep-th
keywords mathcalgravitinoanalyticgaugeharmonicprepotentialsalphacoordinates
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We present the harmonic superspace formulation of $\mathcal{N}=2$ gravitino multiplet, the simplest $\mathcal{N}=2$ half-integer spin gauge supermultiplet. It is shown that, quite similar to other $\mathcal{N}=2$ gauge multiplets, the gravitino supermultiplet is described by unconstrained analytic prepotentials $h^{++\alpha}$ and $h^{+++}$ which contain a conformal gravitino in the Wess-Zumino gauge. The analytic prepotentials naturally come out from the study of $\mathcal{N}=2$ supercurrents associated with hidden symmetries of $\mathcal{N}=2$ vector-hypermultiplet system. We construct the covariant $\mathcal{N}=2$ superfield strengths and the invariant $\mathcal{N}=2$ superfield actions and sketch their component contents. We observe that, at cost of introducing new auxiliary coordinates $\Psi^\alpha$ and $\omega^+$, the gravitino analytic prepotentials acquire a nice geometric interpretation as extra veilbeins of the covariant harmonic derivative $\mathfrak{D}^{++}$. We speculate on a possible origin of the additional coordinates, including their relationship with $\mathcal{N}=2$ supertwistors.

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Cited by 4 Pith papers

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

  1. Structure of $\mathcal{N} = 2$ superfield higher-spin abelian cubic interactions

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    The structure of N=2 abelian cubic higher-spin vertices is fully determined by three analytic supercurrents, and odd-spin (s,1,1) gauge transformations reduce to supersymmetric zilch symmetries.

  2. Linearized $\mathcal{N}=2$ conformal supergravity in the harmonic approach

    hep-th 2025-11 conditional novelty 6.0 of 10

    The first harmonic-superspace action for linearized N=2 conformal supergravity is constructed and shown to be superconformally invariant in both harmonic and chiral superspaces.

  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.

  4. Supersymmetry at BLTP: Recent Progress in Two Directions

    hep-th 2026-06 unverdicted novelty 1.0 of 10

    A self-review of the BLTP supersymmetry group's recent results in N=2 harmonic-superspace higher-spin models and 6D supersymmetric effective actions.

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