75,343 research outputs found
Foliated Structure of The Kuranishi Space and Isomorphisms of Deformation Families of Compact Complex Manifolds
Consider the following uniformization problem. Take two holomorphic
(parametrized by some analytic set defined on a neighborhood of in , for some ) or differentiable (parametrized by an open neighborhood
of in , for some ) deformation families of compact complex
manifolds. Assume they are pointwise isomorphic, that is for each point of
the parameter space, the fiber over of the first family is biholomorphic to
the fiber over of the second family. Then, under which conditions are the
two families locally isomorphic at 0? In this article, we give a sufficient
condition in the case of holomorphic families. We show then that, surprisingly,
this condition is not sufficient in the case of differentiable families. We
also describe different types of counterexamples and give some elements of
classification of the counterexamples. These results rely on a geometric study
of the Kuranishi space of a compact complex manifold
Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras
This paper completes a series devoted to explicit constructions of
finite-dimensional irreducible representations of the classical Lie algebras.
Here the case of odd orthogonal Lie algebras (of type B) is considered (two
previous papers dealt with C and D types). A weight basis for each
representation of the Lie algebra o(2n+1) is constructed. The basis vectors are
parametrized by Gelfand--Tsetlin-type patterns. Explicit formulas for the
matrix elements of generators of o(2n+1) in this basis are given. The
construction is based on the representation theory of the Yangians. A similar
approach is applied to the A type case where the well-known formulas due to
Gelfand and Tsetlin are reproduced.Comment: 29 pages, Late
The string swampland constraints require multi-field inflation
An important unsolved problem that affects practically all attempts to
connect string theory to cosmology and phenomenology is how to distinguish
effective field theories belonging to the string landscape from those that are
not consistent with a quantum theory of gravity at high energies (the "string
swampland"). It was recently proposed that potentials of the string landscape
must satisfy at least two conditions, the "swampland criteria", that severely
restrict the types of cosmological dynamics they can sustain. The first
criterion states that the (multi-field) effective field theory description is
only valid over a field displacement (in units where the Planck mass is 1), measured as a distance in the
target space geometry. A second, more recent, criterion asserts that, whenever
the potential is positive, its slope must be bounded from below, and
suggests . A recent analysis
concluded that these two conditions taken together practically rule out
slow-roll models of inflation. In this note we show that the two conditions
rule out inflationary backgrounds that follow geodesic trajectories in field
space, but not those following curved, non-geodesic, trajectories (which are
parametrized by a non-vanishing bending rate of the multi-field
trajectory). We derive a universal lower bound on (relative to the
Hubble parameter ) as a function of and the number of efolds
, assumed to be at least of order 60. If later studies confirm and
to be strictly , the bound implies strong turns with
. Slow-roll inflation in the landscape is not
ruled out, but it is strongly multi-field.Comment: v1: 15 pages; v2: 16 pages, references added, improved discussions,
version accepted for publication in JCA
Tropicalization of the moduli space of stable maps
Let be an algebraic variety and let be a tropical variety associated
to . We study the tropicalization map from the moduli space of stable maps
into to the moduli space of tropical curves in . We prove that it is a
continuous map and that its image is compact and polyhedral. Loosely speaking,
when we deform algebraic curves in , the associated tropical curves in
deform continuously; moreover, the locus of realizable tropical curves inside
the space of all tropical curves is compact and polyhedral. Our main tools are
Berkovich spaces, formal models, balancing conditions, vanishing cycles and
quantifier elimination for rigid subanalytic sets.Comment: I improved the theorems using parametrized tropical curves in
Mathematische Zeitschrift, 201
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