100,785 research outputs found
The Sen Limit
F-theory compactifications on elliptic Calabi-Yau manifolds may be related to
IIb compactifications by taking a certain limit in complex structure moduli
space, introduced by A. Sen. The limit has been characterized on the basis of
SL(2,Z) monodromies of the elliptic fibration. Instead, we introduce a stable
version of the Sen limit. In this picture the elliptic Calabi-Yau splits into
two pieces, a P^1-bundle and a conic bundle, and the intersection yields the
IIb space-time. We get a precise match between F-theory and perturbative type
IIb. The correspondence is holographic, in the sense that physical quantities
seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as
expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds
to summing up the D(-1)-instanton corrections to the IIb theory.Comment: 41 pp, 1 figure, LaTe
The Sen limit
F-theory compactifications on elliptic Calabi-Yau manifolds may be related to IIb compactifications by taking a certain limit in complex structure moduli space, introduced by A. Sen. The limit has been characterized on the basis of SL(2, Z) monodromies of the elliptic fibration. Instead, we introduce a stable version of the Sen limit. In this picture the elliptic Calabi-Yau splits into two pieces, a P -bundle and a conic bundle, and the intersection yields the IIb space-time. We get a precise match between F-theory and perturbative type IIb. The correspondence is holographic, in the sense that physical quantities seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds to summing up the D(-1)-instanton corrections to the IIb theory.
On the total mass of closed universes
The total mass, the Witten type gauge conditions and the spectral properties
of the Sen-Witten and the 3-surface twistor operators in closed universes are
investigated. It has been proven that a recently suggested expression
for the total mass density of closed universes is vanishing if and only if the
spacetime is flat with toroidal spatial topology; it coincides with the first
eigenvalue of the Sen-Witten operator; and it is vanishing if and only if
Witten's gauge condition admits a non-trivial solution.
Here we generalize slightly the result above on the zero-mass configurations:
if and only if the spacetime is holonomically trivial with toroidal
spatial topology. Also, we show that the multiplicity of the eigenvalues of the
(square of the) Sen-Witten operator is at least two, and a potentially viable
gauge condition is suggested. The monotonicity properties of through
the examples of closed Bianchi I and IX cosmological spacetimes are also
discussed. A potential spectral characterization of these cosmological
spacetimes, in terms of the spectrum of the Riemannian Dirac operator and the
Sen-Witten and the 3-surface twistor operators, is also indicated.Comment: 14 pages, plenary talk at the `Spanish Relativity Meeting in Portugal
2012', Guimar\~aes 3-7 September; Final version, appearing in General
Relativity and Gravitatio
Efficiency Criteria and the Sen-type Social Welfare Function
Most of the Social Welfare Functions available in the literature are Paretian, that is increase in anybody's income in the society is welfare augmenting. The Sen type social welfare function possesses this property as well. However, Paretianity is normative criteria and might not be accepted by everybody. This paper has demonstrated this problem of Paretianity and proposes an alternative Social Welfare Function.Social Welfare Function, Gini Coefficient, Paretianity
On the Sen limit squared
We introduce a class of F-theory vacua which may be viewed as a
specialization of the so-called fibration, and construct a weak coupling
limit associated with such vacua which we view as the `square' of the Sen
limit. We find that while Sen's limit is naturally viewed as an orientifold
theory, the universal tadpole relation which equates the D3 charge between the
associated F-theory compactification and the limit we construct suggests that
perhaps the limiting theory is in fact an oriented theory compactified on the
base of the F-theory elliptic fibration.Comment: No figure
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