53,942 research outputs found
Congruence Property In Conformal Field Theory
The congruence subgroup property is established for the modular
representations associated to any modular tensor category. This result is used
to prove that the kernel of the representation of the modular group on the
conformal blocks of any rational, C_2-cofinite vertex operator algebra is a
congruence subgroup. In particular, the q-character of each irreducible module
is a modular function on the same congruence subgroup. The Galois symmetry of
the modular representations is obtained and the order of the anomaly for those
modular categories satisfying some integrality conditions is determined.Comment: References are updated. Some typos and grammatical errors are
correcte
The Singular Values of the GOE
As a unifying framework for examining several properties that nominally
involve eigenvalues, we present a particular structure of the singular values
of the Gaussian orthogonal ensemble (GOE): the even-location singular values
are distributed as the positive eigenvalues of a Gaussian ensemble with chiral
unitary symmetry (anti-GUE), while the odd-location singular values,
conditioned on the even-location ones, can be algebraically transformed into a
set of independent -distributed random variables. We discuss three
applications of this structure: first, there is a pair of bidiagonal square
matrices, whose singular values are jointly distributed as the even- and
odd-location ones of the GOE; second, the magnitude of the determinant of the
GOE is distributed as a product of simple independent random variables; third,
on symmetric intervals, the gap probabilities of the GOE can be expressed in
terms of the Laguerre unitary ensemble (LUE). We work specifically with
matrices of finite order, but by passing to a large matrix limit, we also
obtain new insight into asymptotic properties such as the central limit theorem
of the determinant or the gap probabilities in the bulk-scaling limit. The
analysis in this paper avoids much of the technical machinery (e.g. Pfaffians,
skew-orthogonal polynomials, martingales, Meijer -function, etc.) that was
previously used to analyze some of the applications.Comment: Introduction extended, typos corrected, reference added. 31 pages, 1
figur
Generalized modularity matrices
Various modularity matrices appeared in the recent literature on network
analysis and algebraic graph theory. Their purpose is to allow writing as
quadratic forms certain combinatorial functions appearing in the framework of
graph clustering problems. In this paper we put in evidence certain common
traits of various modularity matrices and shed light on their spectral
properties that are at the basis of various theoretical results and practical
spectral-type algorithms for community detection
SU(5)xU(1): a string paradigm of a TOE and its experimental consequences
We present a string-inspired/derived supergravity model based on the flipped
structure supplemented by a minimal set of additional matter
representations such that unification occurs at the string scale
(\sim10^{18}\GeV). This model is complemented by two string supersymmetry
breaking scenaria: the no-scale supergravity model and a
dilaton-induced supersymmetry breaking scenario. Both imply universal soft
supersymmetry breaking parameters: and
m_0=\coeff{1}{\sqrt{3}}m_{1/2}, A=-m_{1/2} respectively. In either case the
models depend on only three parameters: , , and .
We present a comparative study of the sparticle and Higgs spectra of both
models and conclude that even though both can be partially probed at the
Tevatron, LEPII, and HERA, a larger fraction of the parameter space of the
no-scale model is actually accessible. In both cases there is a more
constrained version which allows to determine in terms of
. In the strict no-scale case we find that the value of
determines the sign of (\mu>0:\,m_t\lsim135\GeV,
\mu<0:\,m_t\gsim140\GeV) and whether the lightest Higgs boson mass is above
or below 100\GeV. In the more constrained version of the dilaton scenario,
and m_t\lsim155\GeV, 61\GeV\lsim m_h\lsim91\GeV
follow. Thus, continuing Tevatron top-quark searches and LEPI,II Higgs searches
could probe this restricted scenario completely.Comment: CERN-TH.6926/93, CTP-TAMU-33/93, LaTeX, 33 pages, 11 embedded
figures. Significant numerical correction to the dilaton scenario. Complete
ps file (7943 blocks,3.33MB) available via anonymous ftp from site
tamsun.tamu.edu in directory incoming, filename: CTP-TAMU-33-93.p
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