313 research outputs found
N=4 Characters in Gepner Models, Orbits and Elliptic Genera
We review the properties of characters of the N=4 SCA in the context of a
non-linear sigma model on , how they are used to span the orbits, and how
the orbits produce topological invariants like the elliptic genus. We derive
the same expression for the elliptic genus using three different Gepner
models (, and theories), detailing the orbits and verifying
that their coefficients are given by elementary modular functions. We
also reveal the orbits for the , and theories. We
derive relations for cubes of theta functions and study the function for .Comment: 39 pages; errors corrected in section 6, section 7 added (mixed
Gepner models), ref adde
-theoretic obstructions to bounded -structures
Schlichting conjectured that the negative K-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree . The main results of this paper are that vanishes when is a small stable -category with a bounded t-structure and that vanishes for all when additionally the heart of is noetherian. It follows that Barwick's theorem of the heart holds for nonconnective K-theory spectra when the heart is noetherian. We give several applications, to non-existence results for bounded t-structures and stability conditions, to possible K-theoretic obstructions to the existence of the motivic t-structure, and to vanishing results for the negative K-groups of a large class of dg algebras and ring spectra
-theoretic obstructions to bounded -structures
Schlichting conjectured that the negative K-groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree . The main results of this paper are that vanishes when is a small stable -category with a bounded t-structure and that vanishes for all when additionally the heart of is noetherian. It follows that Barwick's theorem of the heart holds for nonconnective K-theory spectra when the heart is noetherian. We give several applications, to non-existence results for bounded t-structures and stability conditions, to possible K-theoretic obstructions to the existence of the motivic t-structure, and to vanishing results for the negative K-groups of a large class of dg algebras and ring spectra
Heterotic Weight Lifting
We describe a method for constructing genuinely asymmetric (2,0) heterotic
strings out of N=2 minimal models in the fermionic sector, whereas the bosonic
sector is only partly build out of N=2 minimal models. This is achieved by
replacing one minimal model plus the superfluous E_8 factor by a
non-supersymmetric CFT with identical modular properties. This CFT generically
lifts the weights in the bosonic sector, giving rise to a spectrum with fewer
massless states. We identify more than 30 such lifts, and we expect many more
to exist. This yields more than 450 different combinations. Remarkably, despite
the lifting of all Ramond states, it is still possible to get chiral spectra.
Even more surprisingly, these chiral spectra include examples with a certain
number of chiral families of SO(10), SU(5) or other subgroups, including just
SU(3) x SU(2) x U(1). The number of families and mirror families is typically
smaller than in standard Gepner models. Furthermore, in a large number of
different cases, spectra with three chiral families can be obtained. Based on a
first scan of about 10% of the lifted Gepner models we can construct, we have
collected more than 10.000 distinct spectra with three families, including
examples without mirror fermions. We present an example where the GUT group is
completely broken to the standard model, but the resulting and inevitable
fractionally charged particles are confined by an additional gauge group
factor.Comment: 19 pages, 1 figur
Asymmetric Gepner Models II. Heterotic Weight Lifting
A systematic study of "lifted" Gepner models is presented. Lifted Gepner
models are obtained from standard Gepner models by replacing one of the N=2
building blocks and the factor by a modular isomorphic model on the
bosonic side of the heterotic string. The main result is that after this change
three family models occur abundantly, in sharp contrast to ordinary Gepner
models. In particular, more than 250 new and unrelated moduli spaces of three
family models are identified. We discuss the occurrence of fractionally charged
particles in these spectra.Comment: 46 pages, 17 figure
Polynomial rings of the chiral models
Via explicit diagonalization of the chiral fusion matrices, we
discuss the possibility of representing the fusion ring of the chiral SU(N)
models, at level K=2, by a polynomial ring in a single variable when is odd
and by a polynomial ring in two variables when is even.Comment: 10 pages, LaTex (ioplppt.sty
Supersymmetries in Free Fermionic Strings
Consistent heterotic free fermionic string models are classified in terms of
their number of spacetime supersymmetries, N. For each of the six distinct
choices of gravitino sector, we determine what number of supersymmetries can
survive additional GSO projections. We prove by exhaustive search that only
three of the six can yield N = 1, in addition to the N = 4, 2, or 0 that five
of the six can yield. One choice of gravitino sector can only produce N = 4 or
0. Relatedly, we find that only Z_2, Z_4, and Z_8 twists of the internal
fermions with worldsheet supersymmetry are consistent with N=1 in free
fermionic models. Any other twists obviate N=1.Comment: changes to match journal version; tex, 53 page
Inferring mental states from dynamic faces in adolescents with Autism Spectrum Disorder : insights from eye-tracking
Towards A Topological G_2 String
We define new topological theories related to sigma models whose target space
is a 7 dimensional manifold of G_2 holonomy. We show how to define the
topological twist and identify the BRST operator and the physical states.
Correlation functions at genus zero are computed and related to Hitchin's
topological action for three-forms. We conjecture that one can extend this
definition to all genus and construct a seven-dimensional topological string
theory. In contrast to the four-dimensional case, it does not seem to compute
terms in the low-energy effective action in three dimensions.Comment: 15 pages, To appear in the proceedings of Cargese 2004 summer schoo
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