101 research outputs found
Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras
We prove the existence and associativity of the nonmeromorphic operator
product expansion for an infinite family of vertex operator algebras, the
triplet W-algebras, using results from P(z)-tensor product theory. While doing
this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is
improved and one reference is adde
An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'}
By extending the methods used in our earlier work, in this paper, we present
an explicit realization of logarithmic \mathcal{W}_{p,p'}-modules that have
L(0) nilpotent rank three. This was achieved by combining the techniques
developed in \cite{AdM-2009} with the theory of local systems of vertex
operators \cite{LL}. In addition, we also construct a new type of extension of
, denoted by . Our results confirm several
claims in the physics literature regarding the structure of projective covers
of certain irreducible representations in the principal block. This approach
can be applied to other models defined via a pair screenings.Comment: 18 pages, v2: one reference added, other minor change
A monomial basis for the Virasoro minimal series M(p,p') : the case 1<p'/p<2
Quadratic relations of the intertwiners are given explicitly in two cases of
chiral conformal field theory, and monomial bases of the representation spaces
are constructed by using the Fourier components of the intertwiners. The two
cases are the (p,p')-minimal series for the Virasoro algebra where 1<p'/p<2,
and the level k integrable highest weight modules for the affine Lie algebra
\hat{sl}_2.Comment: Latex, 29 page
Physical Vacuum Properties and Internal Space Dimension
The paper addresses matrix spaces, whose properties and dynamics are
determined by Dirac matrices in Riemannian spaces of different dimension and
signature. Among all Dirac matrix systems there are such ones, which nontrivial
scalar, vector or other tensors cannot be made up from. These Dirac matrix
systems are associated with the vacuum state of the matrix space. The simplest
vacuum system realization can be ensured using the orthonormal basis in the
internal matrix space. This vacuum system realization is not however unique.
The case of 7-dimensional Riemannian space of signature 7(-) is considered in
detail. In this case two basically different vacuum system realizations are
possible: (1) with using the orthonormal basis; (2) with using the
oblique-angled basis, whose base vectors coincide with the simple roots of
algebra E_{8}.
Considerations are presented, from which it follows that the least-dimension
space bearing on physics is the Riemannian 11-dimensional space of signature
1(-)& 10(+). The considerations consist in the condition of maximum vacuum
energy density and vacuum fluctuation energy density.Comment: 19 pages, 1figure. Submitted to General Relativity and Gravitatio
Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves
We define complexes of vector bundles on products of moduli spaces of framed
rank r torsion-free sheaves on the complex projective plane. The top
non-vanishing Chern classes of the cohomology of these complexes yield actions
of the r-colored Heisenberg and Clifford algebras on the equivariant cohomology
of the moduli spaces. In this way we obtain a geometric realization of the
boson-fermion correspondence and related vertex operators.Comment: 36 pages; v2: Definition of geometric Heisenberg operators modified;
v3: Minor typos correcte
The Impact of Non-Equipartition on Cosmological Parameter Estimation from Sunyaev-Zel'dovich Surveys
The collisionless accretion shock at the outer boundary of a galaxy cluster
should primarily heat the ions instead of electrons since they carry most of
the kinetic energy of the infalling gas. Near the accretion shock, the density
of the intracluster medium is very low and the Coulomb collisional timescale is
longer than the accretion timescale. Electrons and ions may not achieve
equipartition in these regions. Numerical simulations have shown that the
Sunyaev-Zel'dovich observables (e.g., the integrated Comptonization parameter
Y) for relaxed clusters can be biased by a few percent. The Y-mass relation can
be biased if non-equipartition effects are not properly taken into account.
Using a set of hydrodynamical simulations, we have calculated three potential
systematic biases in the Y-mass relations introduced by non-equipartition
effects during the cross-calibration or self-calibration when using the galaxy
cluster abundance technique to constraint cosmological parameters. We then use
a semi-analytic technique to estimate the non-equipartition effects on the
distribution functions of Y (Y functions) determined from the extended
Press-Schechter theory. Depending on the calibration method, we find that
non-equipartition effects can induce systematic biases on the Y functions, and
the values of the cosmological parameters Omega_8, sigma_8, and the dark energy
equation of state parameter w can be biased by a few percent. In particular,
non-equipartition effects can introduce an apparent evolution in w of a few
percent in all of the systematic cases we considered. Techniques are suggested
to take into account the non-equipartition effect empirically when using the
cluster abundance technique to study precision cosmology. We conclude that
systematic uncertainties in the Y-mass relation of even a few percent can
introduce a comparable level of biases in cosmological parameter measurements.Comment: 10 pages, 3 figures, accepted for publication in the Astrophysical
Journal, abstract abridged slightly. Typos corrected in version
Combinatorial Identities and Quantum State Densities of Supersymmetric Sigma Models on N-Folds
There is a remarkable connection between the number of quantum states of
conformal theories and the sequence of dimensions of Lie algebras. In this
paper, we explore this connection by computing the asymptotic expansion of the
elliptic genus and the microscopic entropy of black holes associated with
(supersymmetric) sigma models. The new features of these results are the
appearance of correct prefactors in the state density expansion and in the
coefficient of the logarithmic correction to the entropy.Comment: 8 pages, no figures. To appear in the European Physical Journal
Logarithmic intertwining operators and vertex operators
This is the first in a series of papers where we study logarithmic
intertwining operators for various vertex subalgebras of Heisenberg vertex
operator algebras. In this paper we examine logarithmic intertwining operators
associated with rank one Heisenberg vertex operator algebra , of
central charge . We classify these operators in terms of {\em depth}
and provide explicit constructions in all cases. Furthermore, for we
focus on the vertex operator subalgebra L(1,0) of and obtain
logarithmic intertwining operators among indecomposable Virasoro algebra
modules. In particular, we construct explicitly a family of {\em hidden}
logarithmic intertwining operators, i.e., those that operate among two ordinary
and one genuine logarithmic L(1,0)-module.Comment: 32 pages. To appear in CM
Fusion products, Kostka polynomials, and fermionic characters of su(r+1)_k
Using a form factor approach, we define and compute the character of the
fusion product of rectangular representations of \hat{su}(r+1). This character
decomposes into a sum of characters of irreducible representations, but with
q-dependent coefficients. We identify these coefficients as (generalized)
Kostka polynomials. Using this result, we obtain a formula for the characters
of arbitrary integrable highest-weight representations of \hat{su}(r+1) in
terms of the fermionic characters of the rectangular highest weight
representations.Comment: 21 pages; minor changes, typos correcte
The Harish-Chandra isomorphism for reductive symmetric superpairs
We consider symmetric pairs of Lie superalgebras which are strongly reductive
and of even type, and introduce a graded Harish-Chandra homomorphism. We prove
that its image is a certain explicit filtered subalgebra of the Weyl invariants
on a Cartan subspace whose associated graded is the image of Chevalley's
restriction map on symmetric invariants. This generalises results of
Harish-Chandra and V. Kac, M. Gorelik.Comment: 43 pages; v2: substantially improved versio
- …