109 research outputs found
Igusa's p-adic local zeta function associated to a polynomial mapping and a polynomial integration measure
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
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
We show how non-near horizon, non-dilatonic -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
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 . 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 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
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
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
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
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
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 , the D-module
representations of the D(2,1;\alpha) superalgebras are obtained, with
determined in terms of the scaling dimension according to:
for k=4, i.e. the (4,4) supermultiplet,
for k=3, i.e. (3,4,1), and for k=1, i.e. (1,4,3). For
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 . 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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