10,804 research outputs found
Dimensional Mutation and Spacelike Singularities
I argue that string theory compactified on a Riemann surface crosses over at
small volume to a higher dimensional background of supercritical string theory.
Several concrete measures of the count of degrees of freedom of the theory
yield the consistent result that at finite volume, the effective dimensionality
is increased by an amount of order for a surface of genus and volume
in string units. This arises in part from an exponentially growing density
of states of winding modes supported by the fundamental group, and passes an
interesting test of modular invariance. Further evidence for a plethora of
examples with the spacelike singularity replaced by a higher dimensional phase
arises from the fact that the sigma model on a Riemann surface can be naturally
completed by many gauged linear sigma models, whose RG flows approximate time
evolution in the full string backgrounds arising from this in the limit of
large dimensionality. In recent examples of spacelike singularity resolution by
tachyon condensation, the singularity is ultimately replaced by a phase with
all modes becoming heavy and decoupling. In the present case, the opposite
behavior ensues: more light degrees of freedom arise in the small radius
regime. I comment on the emerging zoology of cosmological singularities that
results.Comment: 15 pages, harvmac big. v2: 18 pages, harvmac big; added computation
of density of states and modular invariance check, enhanced discussion of
multiplicity of solutions all sharing the feature of increased density of
states, added reference
Don't Panic! Closed String Tachyons in ALE Spacetimes
We consider closed string tachyons localized at the fixed points of
noncompact nonsupersymmetric orbifolds. We argue that tachyon condensation
drives these orbifolds to flat space or supersymmetric ALE spaces. The decay
proceeds via an expanding shell of dilaton gradients and curvature which
interpolates between two regions of distinct angular geometry. The string
coupling remains weak throughout. For small tachyon VEVs, evidence comes from
quiver theories on D-branes probes, in which deformations by twisted couplings
smoothly connect non-supersymmetric orbifolds to supersymmetric orbifolds of
reduced order. For large tachyon VEVs, evidence comes from worldsheet RG flow
and spacetime gravity. For \IC^2/\IZ_n, we exhibit infinite sequences of
transitions producing SUSY ALE spaces via twisted closed string condensation
from non-supersymmetric ALE spaces. In a -dual description this provides a
mechanism for creating NS5-branes via {\it closed} string tachyon condensation
similar to the creation of D-branes via {\it open} string tachyon condensation.
We also apply our results to recent duality conjectures involving fluxbranes
and the type 0 string.Comment: 48 pages, harvmac big; 13 figures. v2: added references; comment on
gravity regime added to section 5.2. v3: added reference
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An information-based approach to integrating empirical and explanation-based learning
We describe a new approach to integrating explanation-based and empirical learning methods for learning relational concepts. The approach uses an information-based heuristic to evaluate components of a hypothesis that are proposed either by explanation-based or empirical methods. Providing domain knowledge to the integrated system can decrease the amount of search required during learning and increase the accuracy of learned concepts, even when the domain knowledge is incorrect and incomplete and there is noise in the training data
Tension is Dimension
We propose a simple universal formula for the tension of a D-brane in terms
of a regularized dimension of the associated conformal field theory statespace.Comment: 18 pages, harvmac (b), one ref added, one typo fixe
Retrofitting O'Raifeartaigh Models with Dynamical Scales
We provide a method for obtaining simple models of supersymmetry breaking,
with all small mass scales generated dynamically, and illustrate it with
explicit examples. We start from models of perturbative supersymmetry breaking,
such as O'Raifeartaigh and Fayet models, that would respect an symmetry if
their small input parameters transformed as the superpotential does. By
coupling the system to a pure supersymmetric Yang-Mills theory (or a more
general supersymmetric gauge theory with dynamically small vacuum expectation
values), these parameters are replaced by powers of its dynamical scale in a
way that is naturally enforced by the symmetry. We show that supersymmetry
breaking in these models may be straightforwardly mediated to the
supersymmetric Standard Model, obtain complete models of direct gauge
mediation, and comment on related model building strategies that arise in this
simple framework.Comment: 15 pages, harvmac bi
Signal and Noise in Correlation Matrix
Using random matrix technique we determine an exact relation between the
eigenvalue spectrum of the covariance matrix and of its estimator. This
relation can be used in practice to compute eigenvalue invariants of the
covariance (correlation) matrix. Results can be applied in various problems
where one experimentally estimates correlations in a system with many degrees
of freedom, like in statistical physics, lattice measurements of field theory,
genetics, quantitative finance and other applications of multivariate
statistics.Comment: 17 pages, 3 figures, corrected typos, revtex style changed to elsar
The response to the Dieudonné affair in France risks demonising French minority groups in the name of tolerance
The French comedian Dieudonné M’Bala M’Bala has caused controversy in France over the alleged anti-Semitism of his performances. Paul A. Silverstein writes on the wider issues related to anti-Semitism in French society, and why Dieudonné has proved so controversial. He argues that while Dieudonné’s supporters deny the accusations of anti-Semitism, they feed into a broader social and institutional context that can make Jewish citizens feel targeted. There is also a danger that in attacking Dieudonné, the French establishment risks demonising other French minority groups who make up many of his supporters
Seller Liability Under Section 12(2) of the Securities Act of 1933
This Note discusses which persons courts should deem to be sellers under section 12(2) according to their relationships to the challenged transaction. Part II examines the divergent approaches that courts have developed to identify seller status in the absence of legislative history. Part III analyzes the three major approaches and compares the scope of liability under each analysis. Last, part IV concludes that significant differences exist among these approaches and that courts uniformly should adopt a modified version of the proximate cause-substantial factor analysis
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This part examines each of the three approaches in particular situations and compares the results under each approach. This comparison shows first, that the strict privity approach is too narrow and does not sufficiently meet the needs of purchasers; second, that the aiding and abetting approach is too broad and violates the express language of the statute; and last, that the proximate cause-substantial factor approach is the most reasonable and practicable standard for the courts to employ if properly refined
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