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Sergio Ferrara

Publications and source records attributed to Sergio Ferrara.

At least 37 records · Page 2Linked to original sources
arXiv2015

${\cal R}^2$ Supergravity

We formulate $R^2$ pure supergravity as a scale invariant theory built only in terms of superfields describing the geometry of curved superspace. The standard supergravity duals are obtained in both "old" and "new" minimal formulations of auxiliary fields. These theories have massless fields in de Sitter space as they do in their non supersymmetric counterpart. Remarkably, the dual theory of $R^2$ supergravity in the new minimal formulation is an extension of the Freedman model, describing a massless gauge field and a massless chiral multiplet in de Sitter space, with inverse radius proportional to the Fayet-Iliopoulos term. This model can be interpreted as the "de-Higgsed" phase of the dual companion theory of $R+R^2$ supergravity.

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arXiv2015

Observations on the Partial Breaking of $N=2$ Rigid Supersymmetry

We study the partial breaking of $N=2$ rigid supersymmetry for a generic rigid special geometry of $n$ abelian vector multiplets in the presence of Fayet-Iliopoulos terms induced by the Hyper-Kähler momentum map. By exhibiting the symplectic structure of the problem we give invariant conditions for the breaking to occur, which rely on a quartic invariant of the Fayet-Iliopoulos charges as well as on a modification of the $N=2$ rigid symmetry algebra by a vector central charge.

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arXiv2014

Cosmology with Nilpotent Superfields

We discuss N=1 supergravity inflationary models based on two chiral multiplets, the inflaton and the goldstino superfield. Using superconformal methods for these models, we propose to replace the unconstrained chiral goldstino multiplet by the nilpotent one associated with non-linearly realized supersymmetry of the Volkov-Akulov type. In the new cosmological models, the sgoldstino is proportional to a bilinear combination of fermionic goldstinos. It does not acquire any vev, does nor require stabilization, and does not affect the cosmological evolution. We explain a universal relation of these new models to kappa-symmetric super-Dp-brane actions. This modification significantly simplifies a broad class of the presently existing inflationary models based on supergravity and string theory, including the simplest versions of chaotic inflation, the Starobinsky model, a broad class of cosmological attractors, the Higgs inflation, and much more. In particular, this is a step towards a fully supersymmetric version of the string theory axion monodromy inflation. The new construction serves as a simple and manifestly supersymmetric uplifting tool in the KKLT-type string theory landscape.

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arXiv2014

A Search for an N=2 Inflaton Potential

We consider N=2 supergravity theories that have the same spectrum as the R+R^2 supergravity, as predicted from the off-shell counting of degrees of freedom. These theories describe standard N=2 supergravity coupled to one or two long massive vector multiplets. The central charge is not gauged in these models and they have a Minkowski vacuum with N=2 unbroken supersymmetry. The gauge symmetry, being non-compact, is always broken. $α$-deformed inflaton potentials are obtained, in the case of a single massive vector multiplet, with $α=1/3$ and $2/3$. The $α=1$ potential (i.e. the Starobinsky potential) is also obtained, but only at the prize of having a single massive vector and a residual unbroken gauge symmetry. The inflaton corresponds to one of the Cartan fields of the non-compact quaternionic-K{ä}hler cosets.

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arXiv2014

The Imaginary Starobinsky Model and Higher Curvature Corrections

We elaborate on the predictions of the imaginary Starobinsky model of inflation coupled to matter, where the inflaton is identified with the imaginary part of the inflaton multiplet suggested by the Supergravity embedding of a pure R + R^2 gravity. In particular, we study the impact of higher-order curvature terms and show that, depending on the parameter range, one may find either a quadratic model of chaotic inflation or monomial models of chaotic inflation with fractional powers between 1 and 2.

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arXiv2014

The Imaginary Starobinsky Model

The recent detection by the BICEP2 collaboration of a high level of tensor modes seems to exclude the Starobinsky model of inflation. In this paper we show that this conclusion can be avoided: one can embed the Starobinsky model in supergravity and identify the inflaton field with the imaginary (instead of the real) part of the chiral scalaron multiplet in its formulation. Once coupled to matter, the Starobinsky model may then become the chaotic quadratic model with shift symmetry during inflation and is in good agreement with the current data.

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arXiv2014

Iwasawa nilpotency degree of non compact symmetric cosets in N-extended Supergravity

We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU(2)_P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. This allows us to compute the maximal degree of the polynomials for all faithful representations of Lie algebras. In particular the metric coefficients are related to the scalar kinetic terms while the representation of electric and magnetic charges is related to the coupling of scalars to vector field strengths as they appear in the Lagrangian. We consider symmetric scalar manifolds in N-extended supergravity in various space-time dimensions, elucidating various relations with the underlying Jordan algebras and normed Hurwitz algebras. For magic supergravity theories, our results are consistent with the Tits-Satake projection of symmetric spaces and the nilpotency degree turns out to depend only on the space-time dimension of the theory. These results should be helpful within a deeper investigation of the corresponding supergravity theory, e.g. in studying ultraviolet properties of maximal supergravity in various dimensions.

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arXiv2014

On the Gauged Kahler Isometry in Minimal Supergravity Models of Inflation

In this paper we address the question how to discriminate whether the gauged isometry group G_Sigma of the Kahler manifold Sigma that produces a D-type inflaton potential in a Minimal Supergravity Model is elliptic, hyperbolic or parabolic. We show that the classification of isometries of symmetric cosets can be extended to non symmetric Sigma.s if these manifolds satisfy additional mathematical restrictions. The classification criteria established in the mathematical literature are coherent with simple criteria formulated in terms of the asymptotic behavior of the Kahler potential K(C) = 2 J(C) where the real scalar field C encodes the inflaton field. As a by product of our analysis we show that phenomenologically admissible potentials for the description of inflation and in particular alpha-attractors are mostly obtained from the gauging of a parabolic isometry, this being, in particular the case of the Starobinsky model. Yet at least one exception exists of an elliptic alpha-attractor, so that neither type of isometry can be a priori excluded. The requirement of regularity of the manifold Sigma poses instead strong constraints on the alpha-attractors and reduces their space considerably. Curiously there is a unique integrable alpha-attractor corresponding to a particular value of this parameter.

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arXiv2013

On the Topology of the Inflaton Field in Minimal Supergravity Models

We consider global issues in minimal supergravity models where a single field inflaton potential emerges. In a particular case we reproduce the Starobinsky model and its description dual to a certain formulation of R+R^2 supergravity. For definiteness we confine our analysis to spaces at constant curvature, either vanishing or negative. Five distinct models arise, two flat models with respectively a quadratic and a quartic potential and three based on the SU(1,1)/U(1) space where its distinct isometries, elliptic, hyperbolic and parabolic are gauged. Fayet-Iliopoulos terms are introduced in a geometric way and they turn out to be a crucial ingredient in order to describe the de Sitter inflationary phase of the Starobinsky model.

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arXiv2013

Higher Order Corrections in Minimal Supergravity Models of Inflation

We study higher order corrections in new minimal supergravity models of a single scalar field inflation. The gauging in these models leads to a massive vector multiplet and the D-term potential for the inflaton field with a coupling g^{2} ~ 10^{-10}. In the de-Higgsed phase with vanishing g^2, the chiral and vector multiplets are non-interacting, and the potential vanishes. We present generic manifestly supersymmetric higher order corrections for these models. In particular, for a supersymmetric gravity model -R+ R^2 we derive manifestly supersymmetric corrections corresponding to R^n. The dual version corresponds to a standard supergravity model with a single scalar and a massive vector. It includes, in addition, higher Maxwell curvature/scalar interaction terms of the Born-Infeld type and a modified D-term scalar field potential. We use the dual version of the model to argue that higher order corrections do not affect the last 60 e-foldings of inflation; for example the ξR^4 correction is irrelevant as long as ξ< 10^{24}.

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arXiv2013

Dualities Near the Horizon

In 4-dimensional supergravity theories, covariant under symplectic electric-magnetic duality rotations, a significant role is played by the symplectic matrix M(ϕ), related to the coupling of scalars ϕ to vector field-strengths. In particular, this matrix enters the twisted self-duality condition for 2-form field strengths in the symplectic formulation of generalized Maxwell equations in the presence of scalar fields. In this investigation, we compute several properties of this matrix in relation to the attractor mechanism of extremal (asymptotically flat) black holes. At the attractor points with no flat directions (as in the N = 2 BPS case), this matrix enjoys a universal form in terms of the dyonic charge vector Q and the invariants of the corresponding symplectic representation RQ of the duality group G, whenever the scalar manifold is a symmetric space with G simple and non-degenerate of type E7. At attractors with flat directions, M still depends on flat directions, but not MQ, defining the so-called Freudenthal dual of Q itself. This allows for a universal expression of the symplectic vector field strengths in terms of Q, in the near-horizon Bertotti-Robinson black hole geometry.

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arXiv2013

Vacuum structure in a chiral R+R^n modification of pure supergravity

We discuss an ${\cal R}+{\cal R}^n$ class of modified ${\cal N}=1$, D=4 supergravity models where the deformation is a monomial ${\cal R}^n\big|_F$ in the chiral scalar curvature multiplet ${\cal R}$ of the "old minimal" auxiliary field formulation. The scalaron and goldstino multiplets are dual to each other in this theory. Since one of them is not dynamical, this theory, as recently shown, cannot be used as the supersymmetric completion of $R+R^n$ gravity. This is confirmed by investigating the scalar potential and its critical points in the dual standard supergravity formulation with a single chiral multiplet with specific Kähler potential and superpotential. We study the vacuum structure of this dual theory and we find that there is always a supersymmetric Minkowski critical point which however is pathological for $n\geq 3$ as it corresponds to a corner ($n=3$) and a cusp ($n>3$) point of the potential. For $n>3$ an anti-de Sitter regular supersymmetric vacuum emerges. As a result, this class of models are not appropriate to describe inflation. We also find the mass spectrum and we provide a general formula for the masses of the scalars of a chiral multiplet around the anti-de Sitter critical point and their relation to $osp(1,4)$ unitary representations.

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arXiv2013

Minimal Supergravity Models of Inflation

We present a superconformal master action for a class of supergravity models with one arbitrary function defining the Jordan frame. It leads to a gauge-invariant action for a real vector multiplet, which upon gauge fixing describes a massive vector multiplet, or to a dual formulation with a linear multiplet and a massive tensor field. In both cases the models have one real scalar, the inflaton, naturally suited for single-field inflation. Vectors and tensors required by supersymmetry to complement a single real scalar do not acquire vev's during inflation, so there is no need to stabilize the extra scalars which are always present in the theories with chiral matter multiplets. The new class of models can describe any inflaton potential which vanishes at its minimum and grows monotonically away from the minimum. In this class of supergravity models one can fit any desirable choice of inflationary parameters n_s and r.

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arXiv2013

Constitutive relations, off shell duality rotations and the hypergeometric form of Born-Infeld theory

We review equivalent formulations of nonlinear and higher derivatives theories of electromagnetism exhibiting electric-magnetic duality rotations symmetry. We study in particular on shell and off shell formulations of this symmetry, at the level of action functionals as well as of equations of motion. We prove the conjecture that the action functional leading to Born-Infeld nonlinear electromagnetism, that is duality rotation invariant off shell and that is known to be a root of an algebraic equation of fourth order, is a hypergeometric function.

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arXiv2013

On the Supersymmetric Completion of $R+R^2$ Gravity and Cosmology

We revisit and clarify the supersymmetric versions of $R+ R^2$ gravity, in view of the renewed interest to these models in cosmology. We emphasize that the content of the dual standard supergravity theory in the old minimal formulation necessarily includes two massive chiral multiplets, that we call the inflaton and the goldstino. We point out that the presence of these multiplets is model independent in the old minimal formulation and therefore any theory that contains a single chiral multiplet fails to be a supersymmetric generalization of the $R+R^2$ gravity. The supergravity interactions of the two chiral multiplets are encoded in a superpotential mass term and an arbitrary Kahler potential for the goldstino multiplet. The implication for cosmology of the supersymmetric $R+R^2$ gravity is also discussed.

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arXiv2013

Supersymmetry Breaking by Higher Dimension Operators

We discuss a supersymmetry breaking mechanism for N = 1 theories triggered by higher dimensional op- erators. We consider such operators for real linear and chiral spinor superfields that break superymmetry and reduce to the Volkov-Akulov action. We also consider supersymmetry breaking induced by a higher dimensional operator of a nonminimal scalar (complex linear) multiplet. The latter differs from the stan- dard chiral multiplet in its auxiliary sector, which contains, in addition to the complex scalar auxiliary of a chiral superfield, a complex vector and two spinors auxiliaries. By adding an appropriate higher di- mension operator, the scalar auxiliary may acquire a nonzero vev triggering spontaneous supersymmetry breaking. We find that the spectrum of the theory in the supersymmetry breaking vacuum consists of a free chiral multiplet and a constraint chiral superfield describing the goldstino. Interestingly, the latter turns out to be one of the auxiliary fermions, which becomes dynamical in the supersymmetry breaking vacuum. In all cases we are considering here, there is no sgoldstino mode and thus the goldstino does not have a superpartner. The sgoldstino is decoupled since the goldstino is one of the auxiliaries, which is propagating only in the supersymmetry breaking vacuum. We also point out how higher dimension operators introduce a potential for the propagating scalar of the theory.

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arXiv2013

Constitutive relations and Schroedinger's formulation of nonlinear electromagnetic theories

We present a systematic study of nonlinear and higher derivatives extensions of electromagnetism. We clarify when action functionals S[F] can be explicitly obtained from arbitrary (not necessarily self-dual) nonlinear equations of motion. We show that the "Deformed twisted self-duality condition" proposal originated in the context of supergravity counterterms is actually the general framework needed to discuss self-dual theories starting from a variational principle. We generalize to nonlinear and higher derivatives theories Schroedinger formulation of Born-Infeld theory, and for the latter, and more in general for nonlinear theories, we derive a closed form expression of the corresponding deformed twisted self-duality conditions. This implies that the hypergeometric expression entering these duality conditions and leading to Born-Infeld theory satisfies a hidden quartic equation.

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