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Gauged Supergravity

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Supergravity

Part of the book series: Lecture Notes in Physics ((LNP,volume 991))

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Abstract

In the previous chapter, we discussed the consequences of extended supersymmetry for the geometries of the scalar manifolds in supergravity. Some parts of these geometrical structures are caused by the larger R-symmetry groups, whereas others can be traced back to the electric–magnetic duality of the vector field sector.

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Notes

  1. 1.

    As described in Chap. 6, in \(\mathcal {N}=1\) supergravity this is also true for any Fayet–Iliopoulos constants, as they entail gaugings of the U(1) R-symmetry group that act on the fermions.

  2. 2.

    This follows straightforwardly from (9.15), recalling that for a contravariant vector \(V^{i\prime } = \frac {\partial \varphi ^{i\prime }}{\partial {\varphi ^j}} V^j \simeq \left (\delta ^i_j + \epsilon \frac {\partial k^i}{\partial \varphi ^j} + O(\epsilon ^2)\right )V^j\) and that a covariant vector transform with the inverse Jacobian.

  3. 3.

    We should note that in some instances there may be additional global symmetries that act trivially on the scalar manifolds and that there are also examples where there is still a restricted non-trivial duality group in models without scalar fields, like pure \(\mathcal {N}=2\) supergravity. In most of these cases, the additional factors come from the R-symmetry acting non-trivially on the fermion fields of the theory.

  4. 4.

    Sometimes these terms are referred to as mass terms, because when the scalar fields pick a vacuum expectation value they indeed generate masses for the fermion fields.

  5. 5.

    Actually one should enlarge the possible transformations to all automorphisms of the U-duality group. While this coincides with the U-duality group itself in most cases, there are instances where additional discrete factors become relevant. A particularly relevant example is maximal supergravity, where there is an additional \({\mathbb Z}_2\) parity symmetry that can be used.

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Authors and Affiliations

  1. Physics and Astronomy, University of Padua, Padua, Italy

    Gianguido Dall’Agata

  2. Hamburg, Germany

    Marco Zagermann

Authors
  1. Gianguido Dall’Agata
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  2. Marco Zagermann
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Dall’Agata, G., Zagermann, M. (2021). Gauged Supergravity. In: Supergravity. Lecture Notes in Physics, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-63980-1_9

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  • DOI: https://doi.org/10.1007/978-3-662-63980-1_9

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  • Print ISBN: 978-3-662-63978-8

  • Online ISBN: 978-3-662-63980-1

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