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S. Ferrara

Publications and source records attributed to S. Ferrara.

At least 145 records · Page 8Linked to original sources
arXiv1997

E_{7(7)} Duality, BPS Black-Hole Evolution and Fixed Scalars

We study the general equations determining BPS Black Holes by using a Solvable Lie Algebra representation for the homogenous scalar manifold U/H of extended supergravity. In particular we focus on the N=8 case and we perform a general group theoretical analysis of the Killing spinor equation enforcing the BPS condition. Its solutions parametrize the U-duality orbits of BPS solutions that are characterized by having 40 of the 70 scalars fixed to constant values. These scalars belong to hypermultiplets in the N=2 decomposition of the N=8 theory. Indeed it is shown that those decompositions of the Solvable Lie algebra into appropriate subalgebras which are enforced by the existence of BPS black holes are the same that single out consistent truncations of the N=8 theory to intereacting theories with lower supersymmetry. As an exemplification of the method we consider the simplified case where the only non-zero fields are in the Cartan subalgebra H of Solv(U/H) and correspond to the radii of string toroidal compactification. Here we derive and solve the mixed system of first and second order non linear differential equations obeyed by the metric and by the scalar fields. So doing we retrieve the generating solutions of heterotic black holes with two charges. Finally, we show that the general N=8 generating solution is based on the 6 dimensional solvable subalgebra Solv [(SL(2,\IR) /U(1))^3].

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arXiv1997

R--R Scalars, U--Duality and Solvable Lie Algebras

We consider the group theoretical properties of R--R scalars of string theories in the low-energy supergravity limit and relate them to the solvable Lie subalgebra $\IG_s\subset U$ of the U--duality algebra that generates the scalar manifold of the theory: $\exp[\IG_s]= U/H$. Peccei-Quinn symmetries are naturally related with the maximal abelian ideal ${\cal A} \subset \IG_s $ of the solvable Lie algebra. The solvable algebras of maximal rank occurring in maximal supergravities in diverse dimensions are described in some detail. A particular example of a solvable Lie algebra is a rank one, $2(h_{2,1}+2)$--dimensional algebra displayed by the classical quaternionic spaces that are obtained via c-map from the special Kählerian moduli spaces of Calabi-Yau threefolds.

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arXiv1997

U-Invariants, Black-Hole Entropy and Fixed Scalars

The absolute (moduli-independent) U-invariants of all N>2 extended supergravities at D=4 are derived in terms of (moduli-dependent) central and matter charges. These invariants give a general definition of the ``topological'' Bekenstein-Hawking entropy formula for extremal black-holes and reduce to the square of the black-hole ADM mass for ``fixed scalars'' which extremize the black-hole ``potential'' energy. The Hessian matrix of the black-hole potential at ``fixed scalars'', in contrast to N=2 theories, is shown to be degenerate, with rank (N-2)(N-3) + 2 n (N being the number of supersymmetries and n the number of matter multiplets) and semipositive definite.

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arXiv1996

Solvable Lie Algebras in Type IIA, Type IIB and M Theories

We study some applications of solvable Lie algebras in type IIA, type IIB and M theories. RR and NS generators find a natural geometric interpretation in this framework. Special emphasis is given to the counting of the abelian nilpotent ideals (translational symmetries of the scalar manifolds) in arbitrary D dimensions. These are seen to be related, using Dynkin diagram techniques, to one-form counting in D+1 dimensions. A recipy for gauging isometries in this framework is also presented. In particular, we list the gauge groups both for compact and translational isometries. The former agree with some results already existing in gauged supergravity. The latter should be possibly related to the study of partial supersymmetry breaking, as suggested by a similar role played by solvable Lie algebras in N=2 gauged supergravity.

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arXiv1996

Central Extension of Extended Supergravities in Diverse Dimensions

We generalize central-charge relations and differential identities of N=2 Special Geometry to N extended supergravity in any dimension 4 \leq D <10, and p-extended objects. We study the extremization of the ADM mass per unit of p-volume of BPS extended objects. Runaway solutions for a ``dilaton'' degree of freedom leading to a vanishing result are interpreted as BPS extremal states having vanishing Bekenstein-Hawking Entropy.

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arXiv1996

N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map

The general form of N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows to cover theories difficult to formulate within superspace or tensor calculus approach. We provide the complete lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Lagrangians for rigid theories are also written in this general setting and the connection with local theories elucidated. The derivation of these results using geometrical techniques is briefly summarized.

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arXiv1996

General Matter Coupled N=2 Supergravity

The general form of N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows to cover theories difficult to formulate within superspace or tensor calculus approach. We provide the complete lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Our results can be used to explore properties of theories admitting $N=2$ supergravity as low energy limit.

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arXiv1996

A Search for Non-Perturbative Dualities of Local $N=2$ Yang--Mills Theories from Calabi--Yau Threefolds

The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are connected with the analogous dualities associated with the dynamical Riemann surface of the rigid theory. N=2 rigid gauge theories are reviewed in a framework ready for comparison with the local case. As a byproduct we give in general the full duality group (quantum monodromy) for an arbitrary rigid $SU(r+1)$ gauge theory, extending previous explicit constructions for the $r=1,2$ cases. In the coupling to gravity, R--symmetry and monodromy groups of the dynamical Riemann surface, whose structure we discuss in detail, are embedded into the symplectic duality group $Γ_D$ associated with the moduli space of the dynamical Calabi--Yau threefold.

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arXiv1995

Spontaneous Breaking of N=2 to N=1 in Rigid and Local Supersymmetric Theories

We analyze the relation between rigid and local supersymmetric N=2 field theories, when half of the supersymmetries are spontaneously broken. In particular, we show that the recently found partial supersymmety breaking induced by electric and magnetic Fayet-Iliopoulos terms in rigid theories can be obtained by a suitable flat limit of previously constructed N=2 supergravity models with partial super-Higgs in the observable sector.

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arXiv1995

N=2 Heterotic Superstring and its Dual Theory in Five Dimensions

We study quantum effects in five dimensions in heterotic superstring theory compactified on K_3 x S_1 and analyze the conjecture that its dual effective theory is eleven-dimensional supergravity compactified on a Calabi-Yau threefold. This theory is also equivalent to type II superstring theory compactified on the same Calabi-Yau manifold, in an appropriate large volume limit. In this limit the conifold singularity disappears and is replaced by a singularity associated to enhanced gauge symmetries, as naively expected from the heterotic description. Furthermore, we exhibit the existence of additional massless states which appear in the strong coupling regime of the heterotic theory and are related to a different type of singular points on Calabi-Yau threefolds.

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arXiv1995

R-Symmetry and the Topological Twist of N=2 Effective Supergravities of Heterotic Strings

We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R-symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the tree-level classical special manifolds $ST(n)=SU(1,1)/U(1)\times SO(2,n)/(SO(2)$ $\times SO(n))$ R-symmetry with the specified properties is a continuous symmetry, but for the quantum corrected manifolds ${\hat {ST}}(n)$ a discrete R--group of electric--magnetic duality rotations is sufficient and we argue that it exists.

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arXiv1995

Duality Symmetries in N=2 Heterotic Superstring

We review the derivation and the basic properties of the perturbative prepotential in N=2 compactifications of the heterotic superstring. We discuss the structure of the perturbative monodromy group and the embedding of rigidly supersymmetric monodromies associated with enhanced gauge groups, at both perturbative and non-perturbative level.

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arXiv1995

Minimal Higgs Branch for the Breaking of Half of the Supersymmetries in N=2 Supergravity

It is shown that the minimal Higgs sector of a generic N=2 supergravity theory with unbroken N=1 supersymmetry must contain a Higgs hypermultiplet and a vector multiplet. When the multiplets parametrize the quaternionic manifold SO(4,1)/SO(4), and the special Kahler manifold SU(1,1)/U(1), respectively, a vanishing vacuum energy with a sliding massive spin 3/2 multiplet is obtained. Potential applications to N=2 low energy effective actions of superstrings are briefly discussed.

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arXiv1995

The Symplectic Structure of N=2 Supergravity and its Central Extension

We report on the formulation of $N=2$ $D=4$ supergravity coupled to $n_V$ abelian vector multiplets in presence of electric and magnetic charges. General formulae for the (moduli dependent) electric and magnetic charges for the $n_V+1$ gauge fields are given which reflect the symplectic structure of the underlying special geometry. The specification to Type IIB strings compactified on Calabi-Yau manifolds, with gauge group $U(1)^{h_{21}+1}$ is given.

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arXiv1995

Second-Quantized Mirror Symmetry

We propose and give strong evidence for a duality relating Type II theories on Calabi-Yau spaces and heterotic strings on $K3 \times T^2$, both of which have $N=2$ spacetime supersymmetry. Entries in the dictionary relating the dual theories are derived from an analysis of the soliton string worldsheet in the context of $N=2$ orbifolds of dual $N=4$ compactifications of Type II and heterotic strings. In particular we construct a pairing between Type II string theory on a self-mirror Calabi-Yau space $X$ with $h^{11}= h^{21}= 11$ and a $(4,0)$ background of heterotic string theory on $K3\times T^2$. Under the duality transformation the usual first-quantized mirror symmetry of $X$ becomes a second-quantized mirror symmetry which determines nonperturbative quantum effects. This enables us to compute the exact quantum moduli space. Mirror symmetry of $X$ implies that the low-energy $N=2$ gauge theory is finite, even at enhanced symmetry points. This prediction is verified by direct computation on the heterotic side. Other branches of the moduli space, and corresponding dual pairs which are not finite $N=2$ theories, are connected to this one via black hole condensation.

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arXiv1995

Perturbative Prepotential and Monodromies in N=2 Heterotic Superstring

We discuss the prepotential describing the effective field theory of N=2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic singularities due to the appearance of charged massless states at particular surfaces in the moduli space of vector multiplets. These singularities modify the classical duality symmetry group which now becomes a representation of the fundamental group of the moduli space minus the singular surfaces. For the simplest two-moduli case, this fundamental group turns out to be a certain braid group and we determine the resulting full duality transformations of the prepotential, which are exact in perturbation theory.

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