# Sergio Ferrara's research while affiliated with CERN and other places

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## Publications (487)

Supergravity theories at allow to formulate the Swampland de Sitter conjectures in the complex field space of scalar components of chiral multiplets. We formulate the refined de Sitter conjecture by using the Kähler invariant ‐function and explore a class of models in the Landscape/Swampland scenario which obey and/or violate such conjectures. Furt...

In these lectures we discuss N-extended conformal supergravity and its spectrum in four dimensions. These theories can be considered as the massless limit of Einstein-Weyl supergravity and by taking into account their enhanced gauge symmetries, we derive their massless spectrum, which in general contains a dipole-ghost graviton multiplet and an N-f...

We discuss the Einstein tensor, the supercurrent and their conservation laws of old and new minimal formulations of supergravity in the superconformal approach. The variation of the action with respect to the gauge field of the $R$-symmetry in the conformal approach (the auxiliary field in the super-Poincar\'{e} action) allows to find the Einstein...

Supergravity theories at D=4 allow to formulate the Swampland de Sitter conjectures in the complex field space of scalar components of chiral multiplets. We formulate the de Sitter and refined de Sitter conjecture by using the K\"ahler invariant ${\cal G}$-function and explore a class of models in the Landscape/Swampland scenario which obey and/or...

A bstract
We discuss the connection between Weyl ² supergravity and superstrings and further discuss holography between 4-dimensional, $$ \mathcal{N} $$ N = 4 superconformal Weyl ² supergravity and $$ \mathcal{N} $$ N = 8, higher spin-four theory on AdS 5 . The Weyl ² plus Einstein supergravity theory is a special kind of a bimetric gravity theory...

Some general aspects of supersymmetry and supergravity are briefly reviewed with emphasis on Noether supercurrents and their role in the discussion of supersymmetry breaking.

We discuss the connection between Weyl$^2$ supergravity and superstrings and further discuss holography between 4-dimensional, ${\cal N}=4$ superconformal Weyl$^2$ supergravity and ${\cal N}=8$, higher spin-four theory on $AdS_5$. The massive Weyl$^2$ supergravity theory is a special kind of a bimetric gravity theory and consists of a massless grav...

A bstract
In this paper we study the spectrum of all conformal, $$ \mathcal{N} $$ N -extended supergravities ( $$ \mathcal{N} $$ N = 1, 2, 3, 4) in four space-time dimensions. When these theories are obtained as massless limit of Einstein plus Weyl ² supergravity, the appropriate counting of the enhanced gauge symmetries allow us to derive the mass...

We discuss local supercurrents as sources of the super-Einstein equations in the superconformal approach in the old and new minimal (auxiliary fields) formulation. Modifications of the Ward identity giving the covariant divergence of the Einstein multiplet are considered in presence of a Fayet-Iliopoulos term. Curvature multiplets can be used as al...

A bstract
In the present investigation we consider the possibility of having new massive, higher spin W-supergravity theories, which do not exist as four-dimensional perturbative models. These theories are based on a double copy construction of two supersymmetric field theories, where at least one factor is given by a $$ \mathcal{N}=3 $$ N = 3 fiel...

In this paper we study the spectrum of all conformal, ${\cal N}$-extended supergravities (${\cal N}=1,2,3,4$) in four space-time dimensions. When these theories are obtained as massless limit of Einstein plus Weyl$^2$supergravity, the appropriate counting of the enhanced gauge symmetries allow us to derive the massless spectrum which consist of a d...

In the present investigation we consider the possibility of having new massive, higher spin W-supergravity theories, which do not exist as four-dimensional perturbative models. These theories are based on a double copy construction of two supersymmetric field theories, where at least one factor is given by a N=3 field theory, which is a non-perturb...

We discuss local supercurrents as sources of the super-Einstein equations in the superconformal approach in the old and new minimal (auxiliary fields) formulation. Modifications of the Ward identity giving the covariant divergence of the Einstein multiplet are considered in presence of a Fayet-Iliopoulos term. Curvature multiplets can be used as al...

We consider an expression for the supercurrent in the superconformal formulation of N=1 supergravity. A chiral compensator provides the supersymmetric formulation of the Callan-Coleman-Jackiw (CCJ) improved stress energy tensor, when the conformal gauge is used. Superconformal and non-superconformal matter give different conservation laws of the su...

We identify a cubic holomorphic constraint that subtends the total breaking of \( \mathcal{N} \) = 2 supersymmetry in a vector multiplet and exhibit its microscopic origin. The new constraint leaves behind, at low energies, a vector and the two goldstini, in a non-linear Lagrangian that generalizes the \( \mathcal{N} \) = 2 Volkov-Akulov model.

N=1, D=4 non linear sigma models, parametrized by chiral superfields, usually describe Kaehlerian geometries, provided that Einstein frame supergravity is used. The sigma model metric is no longer Kaehler when local supersymmetry becomes nonlinearly realized through the nilpotency of the supergravity auxiliary fields. In some cases the nonlinear re...

We focus on non-linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive...

We identify a cubic holomorphic constraint that subtends the total breaking of N=2 supersymmetry in a vector multiplet and exhibit its microscopic origin. The new constraint leaves behind, at low energies, a vector and the two goldstini, in a non-linear Lagrangian that generalizes the N=2 Volkov-Akulov model.

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.

We give a new expression for the supercurrent and its conservation in curved ${\cal N}=1$, $D=4$ superspace using the superconformal approach. The first component of the superfield, whose lowest component is the vector auxiliary field gives the (super)Einstein equations. Its trace and couplings to conformal and non-conformal matter is presented. In...

Abdus Salam was a true master of 20th Century Theoretical Physics. Not only was he a pioneer of the Standard Model (for which he shared the Nobel Prize with S. Glashow and S. Weinberg), but he also (co)authored many other outstanding contributions to the field of Fundamental Interactions and their unification. In particular, he was a major contribu...

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.

We consider the dimensional reduction to D = 3 of four maximal-rank supergravities which preserve minimal supersymmetry in D = 11, 7, 5 and 4. Such "curious" theories were investigated some time ago, and the four-dimensional one corresponds to an N = 1 supergravity with 7 chiral multiplets spanning the seven-disk manifold. Recently, this latter the...

Cosmological alpha-attractor models in \cN=1 supergravity are based on hyperbolic geometry of a Poincar\'e disk with the radius square {\cal R}^2=3\alpha. The predictions for the B-modes, r\approx 3\alpha {4\over N^2}, depend on moduli space geometry and are robust for a rather general class of potentials. Here we notice that starting with M-theory...

We derive the mass formulae for ${\cal N}=1$, $D=4$ matter-coupled Supergravity for broken (and unbroken) Supersymmetry in curved space-time. These formulae are applicable to de Sitter configurations as is the case for inflation. For unbroken Supersymmetry in anti-de Sitter (AdS) one gets the mass relations modified by the AdS curvature. We compute...

We prove that all inflationary models, including those with dark energy after the end of inflation, can be embedded in minimal supergravity with a single chiral superfield. Moreover, the amount of supersymmetry breaking is independently tunable due to a degeneracy in the choice for the superpotential. The inflaton is a scalar partner of the Goldsti...

Abdus Salam was a true master of 20th Century Theoretical Physics. Not only was he a pioneer of the Standard Model (for which he shared the Nobel Prize with S. Glashow and S.Weinberg), but he also (co)authored many other outstanding contributions to the field of Fundamental Interactions and their unification. In particular, he was a major contribut...

We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are s...

The c-map of four dimensional non-linear theories of electromagnetism is considered both in the rigid case and in its coupling to gravity. In this way theories with antisymmetric tensors and scalars are obtained, and the three non-linear representations of N = 2 supersymmetry partially broken to N = 1 related. The manifest and covariance of these t...

We elaborate on how to build, in a systematic fashion, two-field Abelian extensions of the Born-Infeld Lagrangian. These models realize the non-trivial duality groups that are allowed in this case, namely U(2), SU(2) and U(1)xU(1). For each class, we also construct an explicit example. They all involve an overall square root and reduce to the Born-...

We study the application of a supersymmetric model with two constrained
supermultiplets to inflationary cosmology. The first superfield S is a
stabilizer chiral superfield satisfying a nilpotency condition of degree 2,
S^2=0. The second superfield Phi is the inflaton chiral superfield, which can
be combined into a real superfield B=(Phi-Phi*)/2i. T...

This review is devoted to highlight some aspects of the relevance of Majorana
fermions in rigid supersymmetry breaking in four spacetime dimensions. After
introducing some basic facts on spinors, and on their symmetries and reality
properties, we consider Goldstino actions describing partial breaking of rigid
supersymmetry, then focussing on Born-I...

In this contribution we describe dual higher-derivative formulations of some cosmological models based on supergravity. Work in this direction started with the R+R2 Starobinsky model, whose supersymmetric extension was derived in the late 80's and was recently revived in view of new CMB data. Models dual to higher-derivative theories are subject to...

We build the minimal supergravity model where the nilpotent chiral goldstino
superfield is coupled to a chiral matter superfield, realising a different
non-linear representation through a mixed nilpotency constraint. The model
describes the spontaneous breaking of local supersymmetry in the presence of a
generically massive Majorana fermion, but in...

Theories with elementary scalar degrees of freedom seem nowadays required for
simple descriptions of the Standard Model and of the Early Universe. It is then
natural to embed theories of inflation in supergravity, also in view of their
possible ultraviolet completion in String Theory. After some general remarks on
inflation in supergravity, we desc...

A scale invariant Goldstino theory coupled to Supergravity is obtained as a
standard supergravity dual of a rigidly scale invariant higher--curvature
Supergravity with a nilpotent chiral scalar curvature. The bosonic part of this
theory describes a massless scalaron and a massive axion in a de Sitter
Universe.

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 c...

We construct Supergravity models where the goldstino multiplet has a
gravitational origin, being dual to the chiral curvature superfield.
Supersymmetry is nonlinearly realized due to a nilpotent constraint, while the
goldstino arises from $\gamma$-traces of the gauge-invariant gravitino field
strength. After duality transformations one recovers, as...

This review is devoted to some aspects of non-linear Supersymmetry in four
dimensions that can be efficiently described via nilpotent superfields, in both
rigid and curved Superspace. Our focus is mainly on the partial breaking of
rigid $N=2$ Supersymmetry and on a class of generalized Born-Infeld systems
that originate from Special Geometry and on...

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...

The self-duality of the N=1 supersymmetric Born--Infeld action implies a
double self-duality of the tensor multiplet square-root action when the scalar
and the antisymmetric tensor are interchanged via Poincare' duality. We show
how this phenomenon extends to D space-time dimensions for non-linear actions
involving pairs of forms of rank p and D-p-...

We consider massive dual pairs of p-forms and (D-p-1)-forms described by
non-linear Lagrangians, where non-linear curvature terms in one theory
translate into non-linear mass-like terms in the dual theory. In particular,
for D=2p and p even the two non-linear structures coincide when the non-linear
massless theory is self-dual. This state of affair...

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-Kahler momentum map. By exhibiting the symplectic structure of the problem we give invariant conditions for the breaking to occur, which rely on a quartic invar...

We investigate $U(1)^{\,n}$ supersymmetric Born-Infeld Lagrangians with a
second non-linearly realized supersymmetry. The resulting non-linear structure
is more complex than the square root present in the standard Born-Infeld
action, and nonetheless the quadratic constraints determining these models can
be solved exactly in all cases containing thr...

We derive new types of U(1)ⁿ Born-Infeld actions based on N = 2 special geometry in four dimensions. As in the single vector multiplet (n = 1) case, the non-linear actions originate, in a particular limit, from quadratic expressions in the Maxwell fields. The dynamics is encoded in a set of coefficients dABC related to the third derivative of the h...

We derive new types of $U(1)^n$ Born-Infeld actions based on N=2 special
geometry in four dimensions. As in the single vector multiplet (n=1) case, the
non--linear actions originate, in a particular limit, from quadratic
expressions in the Maxwell fields. The dynamics is encoded in a set of
coefficients $d_{ABC}$ related to the third derivative of...

Some aspects of black holes in supersymmetric theories of gravity are reviewed and some recent results outlined.

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 co...

The supersymmetric extension of "Starobinsky" $R+\alpha R^2$ models of
inflation is particularly simple in the "new minimal" formalism of
supergravity, where the inflaton has no scalar superpartners. This paper is
devoted to matter couplings in such supergravity models. We show how in the new
minimal formalism matter coupling presents certain featu...

In these lectures, after a short introduction to cosmology, we discuss the
supergravity embedding of higher curvature models of inflation. The
supergravity description of such models is presented for the two different
formulations of minimal supergravity.

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: it is enough to embed the Starobinsky
model in supergravity and identify the inflaton field with the imaginary
(instead of the real) part of the chiral scala...

We construct a supergravity model whose scalar degrees of freedom arise from a chiral superfield and are solely a scalaron and an axion that is very heavy during the inflationary phase. The model includes a second chiral superfield X , which is subject however to the constraint X2=0X2=0 so that it describes only a Volkov–Akulov goldstino and an aux...

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 pa...

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=...

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...

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 polynom...

The global U-dualities of extended supergravity have played a central role in
differentiating the distinct classes of extremal black hole solutions. When the
U-duality group satisfies certain algebraic conditions, as is the case for a
broad class of supergravities, the extremal black holes enjoy a further
symmetry known as Freudenthal duality (F-du...

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 distin...

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 functio...

We report on recent work [4] concerning the determination of the two-centered generic charge orbits of magical \(\mathcal{N} = 2\) and maximal \(\mathcal{N} = 8\) supergravity theories in four dimensions.

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 no...

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...

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...

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, a...

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...

In 4-dimensional supergravity theories, covariant under symplectic electricmagnetic duality rotations, a significant role is played by the symplectic matrix \( \mathcal{M} \)(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 symp...

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 c...

We briefly discuss the foundations of Supergravity as a gauge theory of
supersymmetry, its mathematical structure and the basic lagrangians for
N-extended supersymmetry. As applications, we describe the basic
elements of the supersymmetry breaking mechanism and various aspects of
the physics of extremal black holes.

We propose a first order formalism for multi-centered black holes with flat three-dimensional base-space, within the stu model of N = 2, D = 4 ungauged MaxwellEinstein supergravity. This provides a unified description of first order flows of this universal sector of all models with a symmetric scalar manifold which can be obtained by dimensional re...

We analyze some properties of the four dimensional supergravity theories
which originate from five dimensions upon reduction. They generalize to N>2
extended supersymmetries the d-geometries with cubic prepotentials, familiar
from N=2 special K\"ahler geometry. We emphasize the role of a suitable
parametrization of the scalar fields and the corresp...

We argue that the observed UV finiteness of the 3-loop extended
supergravities may be a manifestation of a hidden local superconformal symmetry
of supergravity. We focus on the SU(2,2|4) dimensionless superconformal model.
In Poincare gauge where the compensators are fixed to phi^2= 6 M_P^2 this model
becomes a pure classical N=4 Einstein supergrav...

We study N=2 supergravity deformed by a genuine supersymmetric completion of the λR
4 term, using the underlying off shell N=2 superconformal framework. The gauge-fixed superconformal model has unbroken local supersymmetry of N=2 supergravity with higher derivative deformation. Elimination of auxiliary fields leads to the deformation of the supersy...

By exploiting the Jordan pair structure of U-duality Lie algebras in D = 3
and the relation to the super-Ehlers symmetry in D = 5, we elucidate the
massless multiplet structure of the spectrum of a broad class of D = 5
supergravity theories. Both simple and semi-simple, Euclidean rank-3 Jordan
algebras are considered. Theories sharing the same boso...

After a brief introduction to the Attractor Mechanism, we review the
appearance of groups of type E7 as generalized electric-magnetic duality
symmetries in locally supersymmetric theories of gravity, with particular
emphasis on the symplectic structure of fluxes in the background of extremal
black hole solutions, with one or two centers. In the lat...

We classify the enhanced helicity symmetry of the Ehlers group to extended
supergravity theories in any dimension. The vanishing character of the
pseudo-Riemannian cosets occurring in this analysis is explained in terms of
Poincar\'e duality. The latter resides in the nature of regularly embedded
quotient subgroups which are non-compact rank preser...

We study properties of D = 4 \( \mathcal{N} \geqslant {2} \) extended supergravities (and related compactifications of superstring theory) and their consistent truncation to the phenomenologically interesting models of \( \mathcal{N} = {1} \) supergravity. This involves a detailed classification of the “degenerations” of the duality groups of type...

Understanding the consequences of the E_{7(7)} duality on the UV properties
of N=8 supergravity requires unravelling when and how duality-covariant actions
can be constructed so as to accommodate duality-invariant counter-terms. For
non-supersymmetric abelian gauge theories exhibiting U(1)-duality, with and
without derivative couplings, it was show...

We present the component Lagrangian for the general coupling of N=1 matter to a higher curvature four-dimensional supergravity in which the (curvature)2 terms enter the Lagrangian only through the Gauss-Bonnet and Hirzebruch invariants. This is the situation suggested by the low-energy limit of heterotic strings, after compactification to four dime...

We explore general properties of matter coupled supergravities with antisymmetric tensor fields embedded in linear multiplets. The four-dimensional supersymmetric version of the Green-Schwarz mechanism leads to the introduction of super Chern-Simons form multiplets whose general component expressions are derived. The use of superconformal technique...

We study general properties of the low-energy effective theory for 4D type II superstrings obtained by the compactification on an abstract (2,2) superconformal system. This is the basic step towards the construction of their moduli space. We give an explicit and general algorithm to convert the effective Lagrangian for the type IIA into that of typ...

We report on some old and new results on the quantum aspects of
four-dimensional maximal supergravity, and its hypothetical ultraviolet
finiteness.

Some aspects of black holes in supersymmetric theories of gravity are
reviewed and some recent results outlined.

We report some results on the relation between extremal black holes in
locally supersymmetric theories of gravity and groups of type E7, appearing as
generalized electric-magnetic duality symmetries in such theories. Some basics
on the covariant approach to the stratification of the relevant symplectic
representation are reviewed, along with a conn...

We consider the interplay of duality symmetries and gauged isometries of supergravity models giving N-extended, spontaneously broken supergravity with a no-scale structure. Some examples motivated by superstring and M-theory compactifications are described.

We study “minimal degree” complete bases of duality- and “horizontal”- invariant homogeneous polynomials in the flux representation of two-centered black hole solutions in two classes of D = 4 Einstein supergravity models with symmetric vector multiplets’ scalar manifolds. Both classes exhibit an SL(2,
\( \mathbb{R} \)) “horizontal” symmetry which...

We relate the mechanism of matter creation in the universe after inflation to
a simple and universal mathematical property of extended N > 1 supergravities
and related compactifications of superstring theory. We show that in all such
models, the inflaton field may decay into vector fields due to a nonminimal
scalar-vector coupling. This coupling is...

We find general relations between the on-shell gravitational trace anomaly
A_N, and the logarithmic correction Delta S_N to the entropy of "large" BPS
extremal black holes in N>1 supergravity theories in D=4 space-time dimensions
(recently computed by Sen [arXiv:1108.3842]). For (generalized) self-mirror
theories (all having A_N = 0), we obtain the...