1,148 research outputs found
Orientifold dual for stuck NS5 branes
We establish T-duality between NS5 branes stuck on an orientifold 8-plane in
type I' and an orientifold construction in type IIB with D7 branes intersecting
at angles. Two applications are discussed. For one we obtain new brane
constructions, realizing field theories with gauge group a product of
symplectic factors, giving rise to a large new class of conformal N=1 theories
embedded in string theory. Second, by studying a D2 brane probe in the type I'
background, we get some information on the still elusive (0,4) linear sigma
model describing a perturbative heterotic string on an ADE singularity.Comment: 24 pages, LaTeX, references adde
Dimers and cluster integrable systems
We show that the dimer model on a bipartite graph on a torus gives rise to a
quantum integrable system of special type - a cluster integrable system. The
phase space of the classical system contains, as an open dense subset, the
moduli space of line bundles with connections on the graph. The sum of
Hamiltonians is essentially the partition function of the dimer model. Any
graph on a torus gives rise to a bipartite graph on the torus. We show that the
phase space of the latter has a Lagrangian subvariety. We identify it with the
space parametrizing resistor networks on the original graph.We construct
several discrete quantum integrable systems.Comment: This is an updated version, 75 pages, which will appear in Ann. Sci.
EN
On hierarchically closed fractional intersecting families
For a set of positive proper fractions and a positive integer ,
a fractional -closed -intersecting family is a collection with the property that for any and
there exists such that
. In this paper we show that for
and any fractional -closed -intersecting family has
size at most linear in , and this is best possible up to a constant factor.
We also show that in the case we have a tight upper bound of
and that a maximal -closed
-intersecting family is determined uniquely up to isomorphism.Comment: 18 pages, 0 figure
Discrete Gauge Symmetries in Discrete MSSM-like Orientifolds
Motivated by the necessity of discrete Z_N symmetries in the MSSM to insure
baryon stability, we study the origin of discrete gauge symmetries from open
string sector U(1)'s in orientifolds based on rational conformal field theory.
By means of an explicit construction, we find an integral basis for the
couplings of axions and U(1) factors for all simple current MIPFs and
orientifolds of all 168 Gepner models, a total of 32990 distinct cases. We
discuss how the presence of discrete symmetries surviving as a subgroup of
broken U(1)'s can be derived using this basis. We apply this procedure to
models with MSSM chiral spectrum, concretely to all known U(3)xU(2)xU(1)xU(1)
and U(3)xSp(2)xU(1)xU(1) configurations with chiral bi-fundamentals, but no
chiral tensors, as well as some SU(5) GUT models. We find examples of models
with Z_2 (R-parity) and Z_3 symmetries that forbid certain B and/or L violating
MSSM couplings. Their presence is however relatively rare, at the level of a
few percent of all cases.Comment: 47 pages. References adde
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