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Generalised Fayet–Iliopoulos Terms in Supergravity

  • PHYSICS OF ELEMENTARY PARTICLES AND ATOMIC NUCLEI. THEORY
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Abstract

The U(1) vector multiplet theory with the Fayet–Iliopoulos (FI) term is one of the oldest and simplest models for spontaneously broken rigid supersymmetry. Lifting the FI term to supergravity requires gauged \(R\)-symmetry, as was first demonstrated in 1977 by Freedman within \(\mathcal{N} = 1\) supergravity. There exists an alternative to the standard FI mechanism, which is reviewed in this conference paper. It is obtained by replacing the FI model with a manifestly gauge-invariant action such that its functional form is determined by two arbitrary real functions of a single complex variable. One of these functions generates a superconformal kinetic term for the vector multiplet, while the other yields a generalised FI term. Coupling such a vector multiplet model to supergravity does not require gauging of the \(R\)-symmetry. These generalised FI terms are consistently defined for any off-shell formulation for \(\mathcal{N} = 1\) supergravity, and are compatible with a supersymmetric cosmological term.

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Notes

  1. For the new minimal formulation [19] the FI term was described in [20].

  2. Since Deser and Zumino [9] made use of supergravity without auxiliary fields, it was next to impossible to construct a complete supergravity-Goldstino action in their setting.

  3. References [25] and [26] appeared in the arXiv within less than a month of each other.

  4. All relevant information concerning the supergravity covariant derivatives \({{\mathcal{D}}_{A}} = \left( {{{\mathcal{D}}_{a}},{{\mathcal{D}}_{\alpha }},{{{\bar {\mathcal{D}}}}^{{\dot {\alpha }}}}} \right)\) and the super-Weyl transformations (with the super-Weyl parameter \(\sigma \) being chiral, \(\mathop {\bar {\mathcal{D}}}\nolimits_{\dot {\alpha }} \sigma = 0\)) can be found in [27].

  5. The constraints (2.13) are invariant under local rescalings \(V \to {{{\text{e}}}^{\rho }}V\), with the parameter \(\rho \) being an arbitrary real scalar superfield. Requiring the action (2.15) to be stationary under such rescalings gives the constraint \(f\Upsilon V = - \tfrac{1}{2}V{{\mathcal{D}}^{\alpha }}{{\mathcal{W}}_{\alpha }} = \) \(\tfrac{1}{8}V{{\mathcal{D}}^{\alpha }}({{\bar {\mathcal{D}}}^{2}} - 4R){{\mathcal{D}}_{\alpha }}V\), where \(f = \xi g{\text{/}}h\). In conjunction with (2.13), this constraint defines the irreducible Goldstino multiplet introduced in [29].

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ACKNOWLEDGMENTS

It is my pleasure to thank the organisers of the Workshop SQS’2019 for their warm hospitality in Yerevan. I am grateful to Darren Grasso and Ulf Lindström for comments on the manuscript. The research presented in this work was supported in part by the Australian Research Council, projects DP160103633 and DP200101944.

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  1. Department of Physics M013, The University of Western Australia, 35 Stirling Highway, 6009, Perth W.A., Australia

    S. M. Kuzenko

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Kuzenko, S.M. Generalised Fayet–Iliopoulos Terms in Supergravity. Phys. Part. Nuclei Lett. 17, 639–644 (2020). https://doi.org/10.1134/S1547477120050234

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