1,234 research outputs found
On the partition sum of the NS five-brane
We study the Type IIA NS five-brane wrapped on a Calabi-Yau manifold X in a
double-scaled decoupling limit. We calculate the euclidean partition function
in the presence of a flat RR 3-form field. The classical contribution is given
by a sum over fluxes of the self-dual tensor field which reduces to a
theta-function. The quantum contributions are computed using a T-dual IIB
background where the five-branes are replaced by an ALE singularity. Using the
supergravity effective action we find that the loop corrections to the free
energy are given by B-model topological string amplitudes. This seems to
provide a direct link between the double-scaled little strings on the
five-brane worldvolume and topological strings. Both the classical and quantum
contributions to the partition function satisfy (conjugate) holomorphic anomaly
equations, which explains an observation of Witten relating topological string
theory to the quantization of three-form fields.Comment: 35 page
Holomorphic matrix models
This is a study of holomorphic matrix models, the matrix models which
underlie the conjecture of Dijkgraaf and Vafa. I first give a systematic
description of the holomorphic one-matrix model. After discussing its
convergence sectors, I show that certain puzzles related to its perturbative
expansion admit a simple resolution in the holomorphic set-up. Constructing a
`complex' microcanonical ensemble, I check that the basic requirements of the
conjecture (in particular, the special geometry relations involving chemical
potentials) hold in the absence of the hermicity constraint. I also show that
planar solutions of the holomorphic model probe the entire moduli space of the
associated algebraic curve. Finally, I give a brief discussion of holomorphic
models, focusing on the example of the quiver, for which I extract
explicitly the relevant Riemann surface. In this case, use of the holomorphic
model is crucial, since the Hermitian approach and its attending regularization
would lead to a singular algebraic curve, thus contradicting the requirements
of the conjecture. In particular, I show how an appropriate regularization of
the holomorphic model produces the desired smooth Riemann surface in the
limit when the regulator is removed, and that this limit can be described as a
statistical ensemble of `reduced' holomorphic models.Comment: 45 pages, reference adde
Branched Matrix Models and the Scales of Supersymmetric Gauge Theories
In the framework of the matrix model/gauge theory correspondence, we consider
supersymmetric U(N) gauge theory with symmetry breaking pattern. Due
to the presence of the Veneziano--Yankielowicz effective superpotential, in
order to satisfy the --term condition , we are forced to
introduce additional terms in the free energy of the corresponding matrix model
with respect to the usual formulation. This leads to a matrix model formulation
with a cubic potential which is free of parameters and displays a branched
structure. In this way we naturally solve the usual problem of the
identification between dimensionful and dimensionless quantities. Furthermore,
we need not introduce the scale by hand in the matrix model. These facts
are related to remarkable coincidences which arise at the critical point and
lead to a branched bare coupling constant. The latter plays the role of the
and scale tuning parameter. We then show that a suitable
rescaling leads to the correct identification of the variables. Finally,
by means of the the mentioned coincidences, we provide a direct expression for
the prepotential, including the gravitational corrections, in terms of
the free energy. This suggests that the matrix model provides a triangulation
of the istanton moduli space.Comment: 1+18 pages, harvmac. Added discussion on the CSW relative shifts of
theta vacua and the odd phases at the critical point. References added and
typos correcte
Baby Universes in String Theory
We argue that the holographic description of four-dimensional BPS black holes
naturally includes multi-center solutions. This suggests that the holographic
dual to the gauge theory is not a single AdS_2 times S^2 but a coherent
ensemble of them. We verify this in a particular class of examples, where the
two-dimensional Yang-Mills theory gives a holographic description of the black
holes obtained by branes wrapping Calabi-Yau cycles. Using the free fermionic
formulation, we show that O(e^{-N}) non-perturbative effects entangle the two
Fermi surfaces. In an Euclidean description, the wave-function of the
multi-center black holes gets mapped to the Hartle-Hawking wave-function of
baby universes. This provides a concrete realization, within string theory, of
effects that can be interpreted as the creation of baby universes. We find
that, at least in the case we study, the baby universes do not lead to a loss
of quantum coherence, in accord with general arguments.Comment: 39 pages, 7 figure
Comments on BRST quantization of strings
The BRST quantization of strings is revisited and the derivation of the path
integral measure for scattering amplitudes is streamlined. Gauge invariances
due to zero modes in the ghost sector are taken into account by using the
Batalin-Vilkovisky formalism. This involves promoting the moduli of Riemann
surfaces to quantum mechanical variables on which BRST transformations act. The
familiar ghost and antighost zero mode insertions are recovered upon
integrating out auxiliary fields. In contrast to the usual treatment, the
gauge-fixed action including all zero mode insertions is BRST invariant.
Possible anomalous contributions to BRST Ward identities due to boundaries of
moduli space are reproduced in a novel way. Two models are discussed
explicitly: bosonic string theory and topological gravity coupled to the
topological A-model.Comment: 23 pages, latex; v2: typos fixed, footnote and reference adde
On Effective Superpotentials and Compactification to Three Dimensions
We study four dimensional N=2 SO/SP supersymmetric gauge theory on R^3\times
S^1 deformed by a tree level superpotential. We will show that the exact
superpotential can be obtained by making use of the Lax matrix of the
corresponding integrable model which is the periodic Toda lattice. The
connection between vacua of SO(2N) and SO(2kN-2k+2) can also be seen in this
framework. Similar analysis can also be applied for SO(2N+1) and SP(2N).Comment: 18 pages, latex file, v2: typos corrected, refs adde
Schaaleffecten en Onderwijskwaliteit
Statistische analyse van data voor het voortgezet onderwijs
laat zien dat er geen eenduidig verband bestaat tussen
schaalgrootte en kwaliteit. Actief overheidsbeleid gericht
op schaalverandering kan volgens dit onderzoek niet
gebaseerd worden op wetenschappelijk bewijs
Competition and educational quality: Evidence from the Netherlands
Ample evidence is available for the effect of competition on educational quality as only a few countries allow large scale competition. In the Netherlands free parental choice is present since the beginning of the 20th century, which can be characterized as a full voucher program with 100% funding. Based on panel data for the Netherlands we show that there is a relation between competition and educational outcomes in secondary education, but that it is negative and small. This effect is larger for small and medium sized schools and for schools which do not have a Protestant or Catholic denomination
Chiral Rings and Anomalies in Supersymmetric Gauge Theory
Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the
chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint
chiral superfield and an arbitrary superpotential. A certain generalization of
the Konishi anomaly leads to an equation which is identical to the loop
equation of a bosonic matrix model. This allows us to solve for the expectation
values of the chiral operators as functions of a finite number of ``integration
constants.'' From this, we can derive the Dijkgraaf-Vafa relation of the
effective superpotential to a matrix model. Some of our results are applicable
to more general theories. For example, we determine the classical relations and
quantum deformations of the chiral ring of super Yang-Mills theory with
SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua
of this theory have a nonzero chiral condensate.Comment: 67 pages, minor change
Combinatorial Identities and Quantum State Densities of Supersymmetric Sigma Models on N-Folds
There is a remarkable connection between the number of quantum states of
conformal theories and the sequence of dimensions of Lie algebras. In this
paper, we explore this connection by computing the asymptotic expansion of the
elliptic genus and the microscopic entropy of black holes associated with
(supersymmetric) sigma models. The new features of these results are the
appearance of correct prefactors in the state density expansion and in the
coefficient of the logarithmic correction to the entropy.Comment: 8 pages, no figures. To appear in the European Physical Journal
- …