6,900 research outputs found
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
On the global symmetries of 6D superconformal field theories
We study global symmetry groups of six-dimensional superconformal field
theories (SCFTs). In the Coulomb branch we use field theoretical arguments to
predict an upper bound for the global symmetry of the SCFT. We then analyze
global symmetry groups of F-theory constructions of SCFTs with a
one-dimensional Coulomb branch. While in the vast majority of cases, all of the
global symmetries allowed by our Coulomb branch analysis can be realized in
F-theory, in a handful of cases we find that F-theory models fail to realize
the full symmetry of the theory on the Coulomb branch. In one particularly
mysterious case, F-theory models realize several distinct maximal subgroups of
the predicted group, but not the predicted group itself.Comment: 47 pages; v2: typos corrected, added the case su(6)* to the analysis
of section 5 and section 6.1. v3: references added, minor changes, published
versio
Recognising Multidimensional Euclidean Preferences
Euclidean preferences are a widely studied preference model, in which
decision makers and alternatives are embedded in d-dimensional Euclidean space.
Decision makers prefer those alternatives closer to them. This model, also
known as multidimensional unfolding, has applications in economics,
psychometrics, marketing, and many other fields. We study the problem of
deciding whether a given preference profile is d-Euclidean. For the
one-dimensional case, polynomial-time algorithms are known. We show that, in
contrast, for every other fixed dimension d > 1, the recognition problem is
equivalent to the existential theory of the reals (ETR), and so in particular
NP-hard. We further show that some Euclidean preference profiles require
exponentially many bits in order to specify any Euclidean embedding, and prove
that the domain of d-Euclidean preferences does not admit a finite forbidden
minor characterisation for any d > 1. We also study dichotomous preferencesand
the behaviour of other metrics, and survey a variety of related work.Comment: 17 page
Asymptotics of the Wigner 9j symbol
We present the asymptotic formula for the Wigner 9j-symbol, valid when all
quantum numbers are large, in the classically allowed region. As in the
Ponzano-Regge formula for the 6j-symbol, the action is expressed in terms of
lengths of edges and dihedral angles of a geometrical figure, but the angles
require care in definition. Rules are presented for converting spin networks
into the associated geometrical figures. The amplitude is expressed as the
determinant of a 2x2 matrix of Poisson brackets. The 9j-symbol possesses
caustics associated with the fold and elliptic and hyperbolic umbilic
catastrophes. The asymptotic formula obeys the exact symmetries of the
9j-symbol.Comment: 17 pages, 7 figure
A Monte-Carlo study of meanders
We study the statistics of meanders, i.e. configurations of a road crossing a
river through "n" bridges, and possibly winding around the source, as a toy
model for compact folding of polymers. We introduce a Monte-Carlo method which
allows us to simulate large meanders up to n = 400. By performing large "n"
extrapolations, we give asymptotic estimates of the connectivity per bridge R =
3.5018(3), the configuration exponent gamma = 2.056(10), the winding exponent
nu = 0.518(2) and other quantities describing the shape of meanders.
Keywords : folding, meanders, Monte-Carlo, treeComment: 12 pages, revtex, 11 eps figure
- …