109 research outputs found

    Igusa's p-adic local zeta function associated to a polynomial mapping and a polynomial integration measure

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    For p prime, we give an explicit formula for Igusa's local zeta function associated to a polynomial mapping f=(f_1,...,f_t): Q_p^n -> Q_p^t, with f_1,...,f_t in Z_p[x_1,...,x_n], and an integration measure on Z_p^n of the form |g(x)||dx|, with g another polynomial in Z_p[x_1,...,x_n]. We treat the special cases of a single polynomial and a monomial ideal separately. The formula is in terms of Newton polyhedra and will be valid for f and g sufficiently non-degenerated over F_p with respect to their Newton polyhedra. The formula is based on, and is a generalization of results of Denef - Hoornaert, Howald et al., and Veys - Zuniga-Galindo.Comment: 20 pages, 5 figures, 2 table

    Effective supergravity descriptions of superstring cosmology

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    This text is a review of aspects of supergravity theories that are relevant in superstring cosmology. In particular, it considers the possibilities and restrictions for `uplifting terms', i.e. methods to produce de Sitter vacua. We concentrate on N=1 and N=2 supergravities, and the tools of superconformal methods, which clarify the structure of these theories. Cosmic strings and embeddings of target manifolds of supergravity theories in others are discussed in short at the end.Comment: 12 pages, contribution to the proceedings of the 2nd international conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelona, July 11-15, 2006, Journal of Physics

    Embedding Branes in Flat Two-time Spaces

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    We show how non-near horizon, non-dilatonic pp-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are found in terms of fields defined in the embedding space, with the constraints enforced by Lagrange multipliers.Comment: LaTex, 8 pages. Contribution to the TMR Conference on Quantum aspects of gauge theories, supersymmetry and unification. Paris, 1-7 September 199

    Jordan Frame Supergravity and Inflation in NMSSM

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    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 Ω(z,zˉ) R\Phi(z, \bar z)\, R. The action is derived by suitably gauge-fixing the superconformal action. The theory has a modified Kaehler geometry, and it exhibits a significant dependence on the frame function Ω(z,zˉ)\Phi (z, \bar 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.Comment: 1+36 pages, 4 figures; v2: discussion updated in Subsec. 4.1, Refs. added, typos fixed. To appear in PR

    The energy and stability of D-term strings

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    Cosmic strings derived from string theory, supergravity or any theory of choice should be stable if we hope to observe them. In this paper we consider D-term strings in D=4, N=1 supergravity with a constant Fayet-Iliopoulos term. We show that the positive deficit angle supersymmetric D-term string is non-perturbatively stable by using standard Witten-Nester techniques to prove a positive energy theorem. Particular attention is paid to the negative deficit angle D-term string, which is known to violate the dominant energy condition. Within the class of string solutions we consider, this violation implies that the negative deficit angle D-term string must have a naked pathology and therefore the positive energy theorem we prove does not apply to it. As an interesting aside, we show that the Witten-Nester charge calculates the total gravitational energy of the D-term string without the need for a cut-off, which may not have been expected.Comment: 18 pages. v2: minor changes and references adde

    Half-BPS cosmic string in N=2 supergravity in the presence of a dilaton

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    We construct new half-BPS cosmic string solutions in D=4 N=2 supergravity compatible with a consistent truncation to N=1 supergravity where they describe D-term cosmic strings. The constant Fayet-Iliopoulos term in the N=1 D-term is not put in by hand but is geometrically engineered by a gauging in the mother N=2 supergravity theory. The coupling of the N=2 vector multiplets is characterized by a cubic prepotential admitting an axion-dilaton field, a common property of many compactifications of string theory. The axion-dilaton field survives the truncation to N=1 supergravity. On the string configuration the BPS equations constrain the dilaton to be an arbitrary constant. All the cosmic string solutions with different values of the dilaton have the same energy per unit length but different lenght scales.Comment: 52 pages; typos correcte

    Superconformal Symmetry, Supergravity and Cosmology

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    We introduce the general N=1 gauge theory superconformally coupled to supergravity. The theory has local SU(2,2|1) symmetry and no dimensional parameters. The superconformal origin of the Fayet-Iliopoulos terms is clarified. The phase of this theory with spontaneously broken conformal symmetry gives various formulations of N=1 supergravity interacting with matter, depending on the choice of the R-symmetry fixing. We have found that the locally superconformal theory is useful for describing the physics of the early universe with a conformally flat FRW metric. Few applications of superconformal theory to cosmology include the study of i) particle production after inflation, particularly the non-conformal helicity 1/2 states of gravitino, ii) the super-Higgs effect in cosmology and the derivation of the equations for the gravitino interacting with any number of chiral and vector multiplets in the gravitational background with varying scalar fields, iii) the weak coupling limit of supergravity and gravitino-goldstino equivalence. This explains why gravitino production in the early universe is not suppressed in the limit of weak gravitational coupling. We discuss the possible existence of an unbroken phase of the superconformal theories, interpreted as a strong coupling limit of supergravity

    Tits-Satake projections of homogeneous special geometries

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    We organize the homogeneous special geometries, describing as well the couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small number of universality classes. This relates manifolds on which similar types of dynamical solutions can exist. The mathematical ingredient is the Tits-Satake projection of real simple Lie algebras, which we extend to all solvable Lie algebras occurring in these homogeneous special geometries. Apart from some exotic cases all the other, 'very special', homogeneous manifolds can be grouped in seven universality classes. The organization of these classes, which capture the essential features of their basic dynamics, commutes with the r- and c-map. Different members are distinguished by different choices of the paint group, a notion discovered in the context of cosmic billiard dynamics of non maximally supersymmetric supergravities. We comment on the usefulness of this organization in universality classes both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.Comment: 65 pages, LaTeX; v2: added reference; v3: small corrections, section 3.3 modifie

    D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics

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    The linear (homogeneous and inhomogeneous) (k, N, N-k) supermultiplets of the N-extended one-dimensional Supersymmetry Algebra induce D-module representations for the N=2,4,8 superconformal algebras. For N=2, the D-module representations of the A(1,0) superalgebra are obtained. For N=4 and scaling dimension \lambda=0, the D-module representations of the A(1,1) superalgebra are obtained. For λ≠0\lambda\neq 0, the D-module representations of the D(2,1;\alpha) superalgebras are obtained, with α\alpha determined in terms of the scaling dimension λ\lambda according to: α=−2λ\alpha=-2\lambda for k=4, i.e. the (4,4) supermultiplet, α=−λ\alpha=-\lambda for k=3, i.e. (3,4,1), and α=λ\alpha=\lambda for k=1, i.e. (1,4,3). For λ≠0\lambda\neq 0 the (2,4,2) supermultiplet induces a D-module representation for the centrally extended sl(2|2) superalgebra. For N=8, the (8,8) root supermultiplet induces a D-module representation of the D(4,1) superalgebra at the fixed value λ=1/4\lambda=1/4. A Lagrangian framework to construct one-dimensional, off-shell, superconformal invariant actions from single-particle and multi-particles D-module representations is discussed. It is applied to explicitly construct invariant actions for the homogeneous and inhomogeneous N=4 (1,4,3) D-module representations (in the last case for several interacting supermultiplets of different chirality).Comment: 22 page
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