arXiv subjects

Pietro Fré

Publications and source records attributed to Pietro Fré.

27 records · Page 2Linked to original sources

arXiv2007

The arrow of time and the Weyl group: all supergravity billiards are integrable

In this paper we show that all supergravity billiards corresponding to sigma-models on any U/H non compact-symmetric space and obtained by compactifying supergravity to D=3 are fully integrable. The key point in establishing the integration algorithm is provided by an upper triangular embedding of the solvable Lie algebra associated with U/H into SL(N,R) which always exists. In this context we establish a remarkable relation between the arrow of time and the properties of the Weyl group. The asymptotic states of the developing Universe are in one-to-one correspondence with the elements of the Weyl group which is a property of the Tits Satake universality classes and not of their single representatives. Furthermore the Weyl group admits a natural ordering in terms of L(T), the number of reflections with respect to the simple roots and the direction of time flows is always towards increasing L(T), which plays the unexpected role of an entropy.

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arXiv2007

Constrained Supermanifolds for AdS M-Theory Backgrounds

A long standing problem is the supergauge completion of AdS_4 x (G/H)_7 or AdS_5 x (G/H)_5 backgrounds which preserve less then maximal supersymmetry. In parallel with the supersolvable realization of the AdS_4 x S^7 background based on Kappa-symmetry, we develop a technique which amounts to solving the above-mentioned problem in a way useful for pure spinor quantization for supermembranes and superstrings. Instead of gauge fixing some of the superspace coordinates to zero, we impose an additional constraint on them reproducing the simplifications of the supersolvable representations. The constraints are quadratic, homogeneous, Sp(4,R)-covariant, and consistent from the quantum point of view in the pure spinor approach. Here we provide the geometrical solution which, in a subsequent work, will be applied to the membrane and the superstring sigma models.

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arXiv2005

Integrability of Supergravity Billiards and the generalized Toda lattice equation

We prove that the field equations of supergravity for purely time-dependent backgrounds, which reduce to those of a one--dimensional sigma model, admit a Lax pair representation and are fully integrable. In the case where the effective sigma model is on a maximally split non--compact coset U/H (maximal supergravity or subsectors of lower supersymmetry supergravities) we are also able to construct a completely explicit analytic integration algorithm, adapting a method introduced by Kodama et al in a recent paper. The properties of the general integral are particularly suggestive. Initial data are represented by a pair C_0, h_0 where C_0 is in the CSA of the Lie algebra of U and h_0 in H/W is in the compact subgroup H modded by the Weyl group of U. At asymptotically early and asymptotically late times the Lax operator is always in the Cartan subalgebra and due to the iso-spectral property the two limits differ only by the action of some element of the Weyl group. Hence the entire cosmic evolution can be seen as a billiard scattering with quantized angles defined by the Weyl group. The solution algorithm realizes a map from H}/W into W.

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arXiv2002

A new first order formalism for k-supersymmetric Born Infeld actions: the D3-brane example

We introduce a new first order formulation of world-volume actions for p-branes with k-supersymmetry. In this language, which involves more auxiliary fields compensated by more local symmetries, the action is provided by a very compact, simple and elegant formula applicable to any supergravity background. The k-supersymmetry variation against which it is invariant is obtained from the bulk supersymmetries by means of a projector that has a simple expression in terms of the auxiliary fields. The distinctive feature of our formalism is that all fermion fields are hidden into the definition of the curvatures and the action is formally the same, in terms of these differential forms as it would be in a purely bosonic theory. Typically our new formulation enables one to discuss the correct boundary actions for non trivial supergravity Dp-brane bulk solutions like the D3-brane solution on smooth ALE manifolds with flux recently constructed in the literature

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arXiv2001

BPS D3-branes on smooth ALE manifolds

In this talk I review the recent construction of a new family of classical BPS solutions of type IIB supergravity describing 3-branes transverse to a 6-dimensional space with topology $\mathbb{R}^{2}\times$ALE. They are characterized by a non-trivial flux of the supergravity 2-forms through the homology 2-cycles of a generic smooth ALE manifold. These solutions have two Killing spinors and thus preserve $\mathcal{N}=2$ supersymmetry. They are expressed in terms of a quasi harmonic function $H$ (the ``warp factor''), whose properties was studied in detail in the case of the simplest ALE, namely the Eguchi-Hanson manifold. The equation for $H$ was identified as an instance of the confluent Heun equation.

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arXiv2001

Gaugings and other supergravity tools of p-brane physics

In this series of lectures I present a review of the geometric structures of supergravity in diverse dimensions mostly relevant to p-brane physics and to pinpoint the correspondence between the macroscopic and microscopic description of branes. In particular I review duality transformations, coset manifold structures and the general steps involved by the process of gauging supergravity lagrangians both with respect to compact, non compact and non semisimple groups. I focus specifically on the issue of the Domain Wall field theory correspondence and its relation with the gaugings of supergravity in p+2 dimensions. A complete review of the geometries involved by D=5, N=2 supergravity and of its most general form is given with emphasis on the problem of finding smooth supersymmetric realizations of the Randall Sundrum scenarios. I also give a general review of the algebraic machinery involved by the Solvable Lie algebra description of the scalar manifolds of supergravity and I emphasize its distinguished role in pinpointing the superstring interpretation of supergravity p brane solutions and the macroscopic/microscopic correspondence.

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arXiv1997

U Duality, Solvable Lie Algebras and Extremal Black-Holes

In this lecture I review recent results on the use of Solvable Lie Algebras as an efficient description of the scalar field sector of supergravities in relation with their non perturbative structure encoded in the U-duality group. I also review recent results on the construction of BPS saturated states as solution of the first differential equations following from imposing preservation of a fraction of the original supersymmetries. In particular I discuss N=2 extremal black holes that are approximated by a Bertotti Robinson metric near their horizon. The extension of this construction to maximally extended supergravities in all dimensions from 4 to 11 is work in progress where the use of the Solvable Lie algebra approach promises to be of decisive usefulness.

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arXiv1996

The Complete Form of N=2 Supergravity and its Place in the General Framework of D=4 N--Extended Supergravities

Relying on the geometrical set up of Special Kähler Geometry and Quaternionic Geometry, which I discussed at length in my Lectures at the 1995 edition of this Spring School, I present here the recently obtained fully general form of N=2 supergravity with completely arbitrary couplings. This lagrangian has already been used in the literature to obtain various results: notably the partial breaking of supersymmetry and various extremal black--hole solutions. My emphasis, however, is only on providing the reader with a completely explicit and ready to use component expression of the supergravity action. All the details of the derivation are omitted but all the definitions of the items entering the lagrangian and the supersymmetry transformation rules are given.

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arXiv1995

Lectures on Special Kahler Geometry and Electric--Magnetic Duality Rotations

In these lectures I review the general structure of electric--magnetic duality rotations in every even space--time dimension. In four dimensions, which is my main concern, I discuss the general issue of symplectic covariance and how it relates to the typical geometric structures involved by N=2 supersymmetry, namely Special Kähler geometry for the vector multiplets and either HyperKähler or Quaternionic geometry for the hypermultiplets. I discuss classical continuous dualities versus non--perturbative discrete dualities. How the moduli space geometry of an auxiliary dynamical Riemann surface (or Calabi--Yau threefold) relates to exact space--time dualities is exemplified in detail for the Seiberg Witten model of an $SU(2)$ gauge theory.

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