We identify a particularly simple class of supergravity models describing superconformal coupling of matter to supergravity. In these models, which we call the canonical superconformal supergravity (CSS) models, the kinetic terms in the Jordan frame are canonical, and the scalar potential is the same as in the global theory. The pure supergravity part of the total action has a local Poincaré supersymmetry, whereas the chiral and vector multiplets coupled to supergravity have a larger local superconformal symmetry.The scale-free globally supersymmetric theories, such as the NMSSM with a scale-invariant superpotential, can be naturally embedded into this class of theories. After the supergravity embedding, the Jordan frame scalar potential of such theories remains scale free; it is quartic, it contains no mass terms, no nonrenormalizable terms, no cosmological constant.The local superconformal symmetry can be broken by additional terms, which, in the small field limit, are suppressed by the gravitational coupling. This can be achieved by introducing the nonminimal scalar-curvature coupling, and by taking into account interactions with a hidden sector.In this approach, the smallness of the mass parameters in the NMSSM may be traced back to the original superconformal invariance. This allows to address the µ-problem and the cosmological domain wall problem in this model, and to implement chaotic inflation in the NMSSM. We discuss the gravitino problem in the NMSSM inflation, as well as the possibility to obtain a broad class of new versions of chaotic inflation in supergravity.

We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 supergravity coupled to n V vector multiplets, in an asymptotically flat extremal black hole background described by a 2 (n V + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold.For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2 (n V + 1)-dimensional representation R V of the U-duality group. Such orbits are non-degenerate, namely they have non-vanishing quartic invariant (for rank-3 spaces). Other than the 1 2 -BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge.The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of V BH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

We present a complete explicit N = 1, d = 4 supergravity action in an arbitrary Jordan frame with non-minimal scalar-curvature coupling of the form Φ(z,z) R. The action is derived by suitably gauge-fixing the superconformal action. The theory has a modified Kähler geometry, and it exhibits a significant dependence on the frame function Φ(z,z) and its derivatives over scalars, in the bosonic as well as in the fermionic part of the action. Under certain simple conditions, the scalar kinetic terms in the Jordan frame have a canonical form.We consider an embedding of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) gauge theory into supergravity, clarifying the Higgs inflation model recently proposed by Einhorn and Jones. We find that the conditions for canonical kinetic terms are satisfied for the NMSSM scalars in the Jordan frame, which leads to a simple action. However, we find that the gauge singlet field experiences a strong tachyonic instability during inflation in this model. Thus, a modification of the model is required to support the Higgs-type inflation.

Abstract:We identify the space of symplectic deformations of maximal gauged supergravity theories. Coordinates of such space parametrize inequivalent supergravity models with the same gauge group. We apply our procedure to the SO(8) gauging, extending recent analyses. We also study other interesting cases, including Cremmer-Scherk-Schwarz models and gaugings of groups contained in SL(8, R) and in SU * (8).

Abstract:The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z = 0, are obtained for the so-called stu model, the minimal rank-3 N = 2 symmetric supergravity in d = 4 space-time dimensions. Comparisons with previous results, as well as the fake supergravity (first order) formalism and an analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane configurations, are given.

We invoke the black hole/qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D = 4 to D = 3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.PACS numbers: 11.25.Mj, 03.65.Ud, 04.70.Dy Keywords: black hole, U-duality, qubit, entanglement Recent work has established some intriguing correspondences between two very different areas of theoretical physics: the entanglement of qubits in quantum information theory (QIT) and black holes in string theory. See [1] for a review. In particular, there is a one-to-one correspondence between the classification of three qubit entanglement [2] and the classification of extremal black holes in the ST U supergravity theory [3,4] that appears in the compactification of string theory from D = 10 to D = 4 dimensions. Moreover, the Bekenstein-Hawking black hole entropy is provided by the three-way entanglement measure.The purpose of this paper is to use this black hole/qubit correspondence to address the much more difficult problem of classifying four-qubit entanglement, currently an active area of research in QIT as experimentalists now control entanglement with four qubits [5]. Although two and three qubit entanglement is wellunderstood, the literature on four qubits can be confusing and seemingly contradictory, as illustrated in Table I. This is due in part to genuine calculational disagreements, but in part to the use of distinct (but in principle consistent and complementary) perspectives on the criteria for classification. On the one hand there is the "covariant" approach which distinguishes the orbits of the equivalence group of Stochastic Local Operations and Classical Communication (SLOCC) by the vanishing or not of covariants/invariants. This philosophy is adopted for the three-qubit case in [2,13], for example, where it was shown that three qubits can be tripartite entangled in two inequivalent ways, denoted W and GHZ (Greenberger-Horne-Zeilinger). The analogous four-qubit case was treated, with partial results, in [14]. On the other hand, there is the "normal form" approach which considers "families" of orbits. Any given state may be transformed into a unique normal form. If the normal form depends on some of the algebraically independent SLOCC invariants it constitutes a family of orbits parametrized by these invariants. On the other hand a parameter-independent family contains a single orbit. This philosophy is adopted for the four-qubit case |Ψ = a ABCD |ABCD A, B, C, D = 0, 1 in [11,12]. Up to permutation of the four qubits, these authors found 6 parameter-dependent families calledFor example, a family of orbits parametrized by all four of the algebraically independent SLOCC invariants is given by the normal form G abcd :(1)To illustrate the difference between these two approaches, consider the separable EPR-EPR state (|00 + |11 ) ⊗ (|00 + |11 ). Since this is obtained by setting b = c = d = 0 in (1) it belongs to the G abcd fa...

We express the d = 4, N = 2 black hole effective potential for cubic holomorphic F functions and generic dyonic charges in terms of d = 5 real special geometry data. The 4d critical points are computed from the 5d ones, and their relation is elucidated. For symmetric spaces, we identify the BPS and non-BPS classes of attractors and the respective entropies. These always derive from simple interpolating formulae between four and five dimensions, depending on the volume modulus and on the 4d magnetic (or electric) charges.

We classify 2-center extremal black hole charge configurations through duality-invariant homogeneous polynomials, which are the generalization of the unique invariant quartic polynomial for single-center black holes based on homogeneous symmetric cubic special Kähler geometries.A crucial role is played by an horizontal SL(p, R) symmetry group, which classifies invariants for p-center black holes. For p = 2, a (spin 2) quintet of quartic invariants emerge. We provide the minimal set of independent invariants for the rank-3 N = 2, d = 4 stu model, and for its lower-rank descendants, namely the rank-2 st 2 and rank-1 t 3 models; these models respectively exhibit seven, six and five independent invariants.We also derive the polynomial relations among these and other duality invariants. In particular, the symplectic product of two charge vectors is not independent from the quartic quintet in the t 3 model, but rather it satisfies a degree-16 relation, corresponding to a quartic equation for the square of the symplectic product itself.