60 research outputs found
Ramond sector of superconformal algebras via quantum reduction
Quantum hamiltonian reduction of affine superalgebras is studied in the
twisted case. The Ramond sector of "minimal" superconformal W-algebras is
described in detail, the determinant formula is obtained. Extensive list of
examples includes all the simple Lie superalgebras of rank up to 2. The paper
generalizes the results of Kac and Wakimoto (math-ph/0304011) to the twisted
case.Comment: 50 pages, 8 figures; v2: examples added, determinant formula
derivation modified, section order change
Coset Construction of Noncompact Spin(7) and G_2 CFTs
We provide a new class of exactly solvable superconformal field theories that
corresponds to type II compactification on manifolds with exceptional
holonomies. We combine N=1 Liouville field and N=1 coset models and construct
modular invariant partition functions of strings moving on these manifolds. The
resulting theories preserve spacetime supersymmetry. Also we explicitly
construct chiral currents in these models to realize consistent string
theories.Comment: 10 pages, LaTeX, no figure. v2: typos corrected, references adde
Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra
In the pattern-of-zeros approach to quantum Hall states, a set of data
{n;m;S_a|a=1,...,n; n,m,S_a in N} (called the pattern of zeros) is introduced
to characterize a quantum Hall wave function. In this paper we find sufficient
conditions on the pattern of zeros so that the data correspond to a valid wave
function. Some times, a set of data {n;m;S_a} corresponds to a unique quantum
Hall state, while other times, a set of data corresponds to several different
quantum Hall states. So in the latter cases, the patterns of zeros alone does
not completely characterize the quantum Hall states. In this paper, We find
that the following expanded set of data {n;m;S_a;c|a=1,...,n; n,m,S_a in N; c
in R} provides a more complete characterization of quantum Hall states. Each
expanded set of data completely characterize a unique quantum Hall state, at
least for the examples discussed in this paper. The result is obtained by
combining the pattern of zeros and Z_n simple-current vertex algebra which
describes a large class of Abelian and non-Abelian quantum Hall states
\Phi_{Z_n}^sc. The more complete characterization in terms of {n;m;S_a;c}
allows us to obtain more topological properties of those states, which include
the central charge c of edge states, the scaling dimensions and the statistics
of quasiparticle excitations.Comment: 42 pages. RevTeX
Generalised discrete torsion and mirror symmetry for G_2 manifolds
A generalisation of discrete torsion is introduced in which different
discrete torsion phases are considered for the different fixed points or twist
fields of a twisted sector. The constraints that arise from modular invariance
are analysed carefully. As an application we show how all the different
resolutions of the T^7/Z_2^3 orbifold of Joyce have an interpretation in terms
of such generalised discrete torsion orbifolds. Furthermore, we show that these
manifolds are pairwise identified under G_2 mirror symmetry. From a conformal
field theory point of view, this mirror symmetry arises from an automorphism of
the extended chiral algebra of the G_2 compactification.Comment: LaTeX, 25 pages, 1 figure; v2: one reference added and comment about
higher loop modular invariance corrected, version to be publishe
The Topological G2 String
We construct new topological theories related to sigma models whose target
space is a seven dimensional manifold of G_2 holonomy. We define a new type of
topological twist and identify the BRST operator and the physical states.
Unlike the more familiar six dimensional case, our topological model is defined
in terms of conformal blocks and not in terms of local operators of the
original theory. We also present evidence that one can extend this definition
to all genera and construct a seven-dimensional topological string theory. We
compute genus zero correlation functions and relate these to Hitchin's
functional for three-forms in seven dimensions. Along the way we develop the
analogue of special geometry for G_2 manifolds. When the seven dimensional
topological twist is applied to the product of a Calabi-Yau manifold and a
circle, the result is an interesting combination of the six dimensional A- and
B-models.Comment: 76 pages, 1 figure, typos correcte
Unitary minimal models of SW(3/2,3/2,2) superconformal algebra and manifolds of G_2 holonomy
The SW(3/2,3/2,2) superconformal algebra is a W algebra with two free
parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2.
The algebra is proved to be the symmetry algebra of the coset
(su(2)+su(2)+su(2))/su(2). At the central charge c=21/2 the algebra coincides
with the superconformal algebra associated to manifolds of G_2 holonomy. The
unitary minimal models of the SW(3/2,3/2,2) algebra and their fusion structure
are found. The spectrum of unitary representations of the G_2 holonomy algebra
is obtained.Comment: 34 pages, 2 figures, latex; v2: added examples in appendix D; v3:
published version, corrected typo
Lineage skewing and genome instability underlie marrow failure in a zebrafish model of GATA2 deficiency
A Realization of N=1 Algebras with Wolf Spaces
We find out that some unitary minimal models of the N=1
superconformal algebra can be realized as the level one coset models based on
the Wolf spaces . We obtain the expression of the
fermionic current with the conformal weight 5/2 in the algebra. Then, these
models are twisted to give the topological conformal field theories.Comment: 7 pages, references added, published versio
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