3,843 research outputs found
A Note on Four-Point Functions in Logarithmic Conformal Field Theory
The generic structure of 4-point functions of fields residing in
indecomposable representations of arbitrary rank is given. The presented
algorithm is illustrated with some non-trivial examples and permutation
symmetries are exploited to reduce the number of free structure-functions,
which cannot be fixed by global conformal invariance alone.Comment: Contribution to the Proceedings of the 37th International Symposium
Ahrenshoop on the Theory of Elementary Particles, 7p
Notes on Generalised Nullvectors in logarithmic CFT
In these notes we discuss the procedure how to calculate nullvectors in
general indecomposable representations which are encountered in logarithmic
conformal field theories. In particular, we do not make use of any of the
restrictions which have been imposed in logarithmic nullvector calculations up
to now, especially the quasi-primarity of all Jordan cell fields.
For the quite well-studied c_{p,1} models we calculate examples of
logarithmic nullvectors which have not been accessible to the older methods and
recover the known representation structure. Furthermore, we calculate
logarithmic nullvectors in the up to now almost unexplored general augmented
c_{p,q} models and use these to find bounds on their possible representation
structures.Comment: 27 pages, 3 figures; v2: Corrected two typos, added one reference to
the conclusio
Logarithmic Primary Fields in Conformal and Superconformal Field Theory
In this note, some aspects of the generalization of a primary field to the
logarithmic scenario are discussed. This involves understanding how to build
Jordan blocks into the geometric definition of a primary field of a conformal
field theory. The construction is extended to N=1,2 superconformal theories.
For the N=0,2 theories, the two-point functions are calculated.Comment: 17 pages LaTeX 2e, references added, journal details adde
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
Indecomposable Representations in Z_n Symmetric b,c Ghost Systems via Deformations of the Virasoro Field
The Virasoro field associated to b,c ghost systems with arbitrary integer
spin lambda on an n-sheeted branched covering of the Riemann sphere is
deformed. This leads to reducible but indecomposable representations, if the
new Virasoro field acts on the space of states, enlarged by taking the tensor
product over the different sheets of the surface. For lambda=1, proven LCFT
structures are made explicit through this deformation. In the other cases, the
existence of Jordan cells is ruled out in favour of a novel kind of
indecomposable representations.Comment: 28 pages, 1 figure, uses empheq.sty, mhtools.sty, mhsetup.st
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
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