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Higher spins in harmonic superspace

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Abstract

We report on a recent progress in constructing off-shell \(4\)D, \(\mathcal{N}=2\) supersymmetric integer higher-superspin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with matter hypermultiplets. For even superspins, a new equivalent representation of the hypermultiplet couplings in terms of an analytic \(\omega\) superfield is presented. It involves both cubic and quartic vertices.

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Notes

  1. Also see [13], [14], where, in particular, the relevant component off- and on-shell Lagrangians are discussed in more detail.

  2. See [19] for a brief review.

  3. The expression for \(V^{--}\) can be obtained either by solving the flatness condition with the help of harmonic distributions (see book [17]) or by a direct calculation in the component formalism, starting from the WZ form of \(V^{++}\).

  4. The complete form of the WZ gauge can be found in [15].

  5. The spinor indices are raised and lowered in the standard way, with the help of the antisymmetric tensor \(\varepsilon_{\mu\nu}\), \({\varepsilon_{12} = -\varepsilon^{12} = 1}\), e.g., \(l_{(\nu}^{\;\;\;\mu)} = \varepsilon_{\nu\rho}l^{(\rho\mu)}\).

  6. Hereafter, all Lorentz indices of the same nature in the coefficients of differential operators are assumed to be properly symmetrized with those hidden in the multi-index \(M\).

  7. This can be easily observed in the simplest spin \(\mathbf{1}\) case.

  8. This change of variables is given in book [17].

  9. We use the standard definitions \((D^+)^2 := D^{+ \alpha}D^+_{\alpha}\), \((\bar{D}^+)^2 := \bar{D}^{+}_{\dot\alpha}\bar{D}^{+\dot\alpha}\), and \((D^+)^4 := \frac{1}{16}(D^+)^2(\bar{D}^+)^2\).

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Acknowledgments

I thank the Organizers of the A. A. Slavnov Memorial Conference for inviting me to give this talk and kind hospitality at the Steklov Mathematical Institute in Moscow. I also thank my coauthors Ioseph Buchbinder and Nikita Zaigraev, on the joint papers with whom this talk is essentially based. I also thank the anonymous referee for the useful remarks aimed at making the exposition more complete and coherent.

Funding

This work was supported by the Russian Science Foundation (project No. 21-12-00129).

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Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia

    E. A. Ivanov

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia

    E. A. Ivanov

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 217, pp. 515–532 https://doi.org/10.4213/tmf10527.

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Ivanov, E.A. Higher spins in harmonic superspace. Theor Math Phys 217, 1855–1869 (2023). https://doi.org/10.1134/S004057792312005X

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