116 research outputs found

### Quasi-rational fusion products

Fusion is defined for arbitrary lowest weight representations of
$W$-algebras, without assuming rationality. Explicit algorithms are given. A
category of quasirational representations is defined and shown to be stable
under fusion. Conjecturally, it may coincide with the category of
representations of finite quantum dimensions.Comment: 10 pages (plain TeX

### The associative algebras of conformal field theory

Modulo the ideal generated by the derivative fields, the normal ordered
product of holomorphic fields in two-dimensional conformal field theory yields
a commutative and associative algebra. The zero mode algebra can be regarded as
a deformation of the latter. Alternatively, it can be described as an
associative quotient of the algebra given by a modified normal ordered product.
We clarify the relation of these structures to Zhu's product and Zhu's algebra
of the mathematical literature.Comment: LaTeX (BibTeX), 6 pages, no figure

### Rational CFTs on Riemann surfaces

The partition function of rational conformal field theories (CFTs) on Riemann
surfaces is expected to satisfy ODEs of Gauss-Manin type. We investigate the
case of hyperelliptic surfaces and derive the ODE system for the $(2,5)$
minimal model.Comment: 90 page

### Mirror Symmetry on Kummer Type K3 Surfaces

We investigate both geometric and conformal field theoretic aspects of mirror
symmetry on N=(4,4) superconformal field theories with central charge c=6. Our
approach enables us to determine the action of mirror symmetry on (non-stable)
singular fibers in elliptic fibrations of Z_N orbifold limits of K3. The
resulting map gives an automorphism of order 4,8, or 12, respectively, on the
smooth universal cover of the moduli space. We explicitly derive the geometric
counterparts of the twist fields in our orbifold conformal field theories. The
classical McKay correspondence allows for a natural interpretation of our
results.Comment: 27 pages, no figures; references added, typos and equation (28)
correcte

### Einstein's cosmology review of 1933: a new perspective on the Einstein-de Sitter model of the cosmos

We present a first English translation and analysis of a little-known review
of relativistic cosmology written by Albert Einstein in late 1932. The article,
which was published in 1933 in a book of Einstein papers translated into
French, contains a substantial review of static and dynamic relativistic models
of the cosmos, culminating in a discussion of the Einstein-de Sitter model. The
article offers a valuable contemporaneous insight into Einstein's cosmology in
the 1930s and confirms that his interest lay in the development of the simplest
model of the cosmos that could account for observation, rather than an
exploration of all possible cosmic models. The article also confirms that
Einstein did not believe that simplistic relativistic models could give an
accurate description of the early universe.Comment: Accepted for publication in the European Physical Journal (H).
Includes an English translation of a little-known review of cosmology written
by Albert Einstein in 1933. 20 pages, 4 figure

### One Hundred Years of the Cosmological Constant: from 'Superfluous Stunt' to Dark Energy

We present a centennial review of the history of the term known as the
cosmological constant. First introduced to the general theory of relativity by
Einstein in 1917 in order to describe a universe that was assumed to be static,
the term fell from favour in the wake of the discovery of the expanding
universe, only to make a dramatic return in recent times. We consider
historical and philosophical aspects of the cosmological constant over four
main epochs: (i) the use of the term in static cosmologies (both Newtonian and
relativistic); (ii) the marginalization of the term following the discovery of
cosmic expansion; (iii) the use of the term to address specific cosmic puzzles
such as the timespan of expansion, the formation of galaxies and the redshifts
of the quasars; (iv) the re-emergence of the term in today's Lamda-CDM
cosmology. We find that the cosmological constant was never truly banished from
theoretical models of the universe, but was sidelined by astronomers for
reasons of convenience. We also find that the return of the term to the
forefront of modern cosmology did not occur as an abrupt paradigm shift due to
one particular set of observations, but as the result of a number of empirical
advances such as the measurement of present cosmic expansion using the Hubble
Space Telescope, the measurement of past expansion using type SN 1a supernovae
as standard candles, and the measurement of perturbations in the cosmic
microwave background by balloon and satellite. We give a brief overview of
contemporary interpretations of the physics underlying the cosmic constant and
conclude with a synopsis of the famous cosmological constant problem.Comment: 60 pages, 6 figures. Some corrections, additions and extra
references. Accepted for publication the European Physical Journal (H

### A General Vanishing Theorem

Let E be a vector bundle and L be a line bundle over a smooth projective variety X. In this article, we give a condition for the vanishing of Dolbeault cohomology groups of the form H^p,q (X, S^Î± E â (â§^ÎČ)E â L) when S^(Î±+ÎČ)E â L is ample. This condition is shown to be invariant under the interchange of p and q. The optimality of this condition is discussed for some parameter values

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