302 research outputs found
Fusion & Tensoring of Conformal Field Theory and Composite Fermion Picture of Fractional Quantum Hall Effect
We propose a new way for describing the transition between two quantum Hall
effect states with different filling factors within the framework of rational
conformal field theory. Using a particular class of non-unitary theories, we
explicitly recover Jain's picture of attaching flux quanta by the fusion rules
of primary fields. Filling higher Landau levels of composite fermions can be
described by taking tensor products of conformal theories. The usual projection
to the lowest Landau level corresponds then to a simple coset of these tensor
products with several U(1)-theories divided out. These two operations -- the
fusion map and the tensor map -- can explain the Jain series and all other
observed fractions as exceptional cases. Within our scheme of transitions we
naturally find a field with the experimentally observed universal critical
exponent 7/3.Comment: 13 pages, LaTeX (or better LaTeX2e), no figures, also available at
http://www.sns.ias.edu/~flohr
Logarithmic Conformal Field Theory - or - How to Compute a Torus Amplitude on the Sphere
We review some aspects of logarithmic conformal field theories which might
shed some light on the geometrical meaning of logarithmic operators. We
consider an approach, put forward by V. Knizhnik, where computation of
correlation functions on higher genus Riemann surfaces can be replaced by
computations on the sphere under certain circumstances. We show that this
proposal naturally leads to logarithmic conformal field theories, when the
additional vertex operator insertions, which simulate the branch points of a
ramified covering of the sphere, are viewed as dynamical objects in the theory.
We study the Seiberg-Witten solution of supersymmetric low energy effective
field theory as an example where physically interesting quantities, the periods
of a meromorphic one-form, can effectively be computed within this conformal
field theory setting. We comment on the relation between correlation functions
computed on the plane, but with insertions of twist fields, and torus vacuum
amplitudes.Comment: LaTeX, 38 pp. 3 figures (provided as eps and as pdf). Contribution to
the Ian Kogan Memorial Volume "From Fields to Strings: Circumnavigating
Theoretical Physics
More Curiosities at Effective c = 1
The moduli space of all rational conformal quantum field theories with
effective central charge c_eff = 1 is considered. Whereas the space of unitary
theories essentially forms a manifold, the non unitary ones form a fractal
which lies dense in the parameter plane. Moreover, the points of this set are
shown to be in one-to-one correspondence with the elements of the modular group
for which an action on this set is defined.Comment: 13 pp. LaTeX with 2 PostScript figures (finally in compressed bitmap
format to save disk space
Operator Product Expansion and Zero Mode Structure in Logarithmic CFT
The generic structure of 1-, 2- and 3-point functions of fields residing in
indecomposable representations of arbitrary rank are given. These in turn
determine the structure of the operator product expansion in logarithmic
conformal field theory. The crucial role of zero modes is discussed in some
detail.Comment: Contribution to the Proceedings of the 36th International Symposium
Ahrenshoop on the Theory of Elementary Particles, 7p
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