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Register a new userSupergravity at 40: Reflections and Perspectives
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Added by
Augusto Sagnotti Prof.
Publication date
2017
fields
Physics
and research's language is
English
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The fortieth anniversary of the original construction of Supergravity provides an opportunity to combine some reminiscences of its early days with an assessment of its impact on the quest for a quantum theory of gravity.
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We review some recent trends in the inflationary model building, the supersymmetry (SUSY) breaking, the gravitino Dark Matter (DM) and the Primordial Black Holes (PBHs) production in supergravity. The Starobinsky inflation can be embedded into supergravity when the inflaton belongs to the massive vector multiplet associated with a (spontaneously broken) $U(1)$ gauge symmetry. The SUSY and R-symmetry can be also spontaneously broken after inflation by the (standard) Polonyi mechanism. Polonyi particles and gravitinos are super heavy and can be copiously produced during inflation via the Schwinger mechanism sourced by the Universe expansion. The overproduction and instability problems can be avoided, and the positive cosmological constant (dark energy) can also be introduced. The observed abundance of the Cold Dark Matter (CDM) composed of gravitinos can be achieved in our supergravity model too, thus providing the unifying framework for inflation, supersymmetry breaking, dark energy and dark matter genesis. Our supergravity approach may also lead to a formation of primordial non-linear structures like stellar-mass-type black holes, and may include the SUSY GUTs inspired by heterotic string compactifications, unifying particle physics with quantum gravity.
We discuss supergravity inflation in braneworld cosmology for the class of potentials $V(phi)=alpha phi^nrm{exp}(-beta^m phi^m)$ with $m=1,~2$. These minimal SUGRA models evade the $eta$ problem due to a broken shift symmetry and can easily accommodate the observational constraints. Models with smaller $n$ are preferred while models with larger $n$ are out of the $2sigma$ region. Remarkably, the field excursions required for $60$ $e$-foldings stay sub-planckian $Deltaphi <1$.
We propose a new construction of the supergravity inflation as an UV completion of the Higgs-$R^2$ inflation. In the dual description of $R^2$-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singlet scalar fields. We also discuss supersymmetry breaking and its transmission to the visible sector as a result of the couplings of the dual chiral superfields and the non-minimal gravity coupling of the Higgs fields.
No-scale supergravity is the appropriate general framework for low-energy effective field theories derived from string theory. The simplest no-scale Kahler potential with a single chiral field corresponds to a compactification to flat Minkowski space with a single volume modulus, but generalizations to single-field no-scale models with de Sitter vacua are also known. In this paper we generalize these de Sitter constructions to two- and multi-field models of the types occurring in string compactifications with more than one relevant modulus. We discuss the conditions for stability of the de Sitter solutions and holomorphy of the superpotential, and give examples whose superpotential contains only integer powers of the chiral fields.
In four spacetime dimensions, all ${cal N} =1$ supergravity-matter systems can be formulated in the so-called $mathsf{U}(1)$ superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background $mathsf{U}(1)$ superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields $ell_{(alpha_1 dots alpha_m) ({dot alpha}_1 dots {dot alpha}_n)}$, with $m$ and $n$ non-negative integers, $m+n>0$, and elaborate on their significance in the following cases: (i) $m=n=1$; (ii) $m-1=n=0$; and (iii) $m=n>1$. The (conformal) Killing vector superfields $ell_{alpha dot alpha}$ generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields $ell_{alpha }$ generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with $m=n>1$ prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.
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