18 research outputs found
Poincare Polynomials and Level Rank Dualities in the Coset Construction
We review the coset construction of conformal field theories; the emphasis is
on the construction of the Hilbert spaces for these models, especially if fixed
points occur. This is applied to the superconformal cosets constructed by
Kazama and Suzuki. To calculate heterotic string spectra we reformulate the
Gepner con- struction in terms of simple currents and introduce the so-called
extended Poincar\'e polynomial. We finally comment on the various equivalences
arising between models of this class, which can be expressed as level rank
dualities. (Invited talk given at the III. International Conference on
Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June
1993. To appear in Theor. Math. Phys.)Comment: 14 pages in LaTeX, HD-THEP-93-4
Automorphisms of the affine SU(3) fusion rules
We classify the automorphisms of the (chiral) level-k affine SU(3) fusion
rules, for any value of k, by looking for all permutations that commute with
the modular matrices S and T. This can be done by using the arithmetic of the
cyclotomic extensions where the problem is naturally posed. When k is divisible
by 3, the automorphism group (Z_2) is generated by the charge conjugation C. If
k is not divisible by 3, the automorphism group (Z_2 x Z_2) is generated by C
and the Altsch\"uler--Lacki--Zaugg automorphism. Although the combinatorial
analysis can become more involved, the techniques used here for SU(3) can be
applied to other algebras.Comment: 21 pages, plain TeX, DIAS-STP-92-4
On parity functions in conformal field theories
We examine general aspects of parity functions arising in rational conformal
field theories, as a result of Galois theoretic properties of modular
transformations. We focus more specifically on parity functions associated with
affine Lie algebras, for which we give two efficient formulas. We investigate
the consequences of these for the modular invariance problem.Comment: 18 pages, no figure, LaTeX2
Scaling functions from q-deformed Virasoro characters
We propose a renormalization group scaling function which is constructed from
q-deformed fermionic versions of Virasoro characters. By comparison with
alternative methods, which take their starting point in the massive theories,
we demonstrate that these new functions contain qualitatively the same
information. We show that these functions allow for RG-flows not only amongst
members of a particular series of conformal field theories, but also between
different series such as N=0,1,2 supersymmetric conformal field theories. We
provide a detailed analysis of how Weyl characters may be utilized in order to
solve various recurrence relations emerging at the fixed points of these flows.
The q-deformed Virasoro characters allow furthermore for the construction of
particle spectra, which involve unstable pseudo-particles.Comment: 31 pages of Latex, 5 figure
Kinks in the Kondo problem
We find the exact quasiparticle spectrum for the continuum Kondo problem of
species of electrons coupled to an impurity of spin . In this
description, the impurity becomes an immobile quasiparticle sitting on the
boundary. The particles are ``kinks'', which can be thought of as field
configurations interpolating between adjacent wells of a potential with
degenerate minima. For the overscreened case , the boundary has this kink
structure as well, which explains the non-integer number of boundary states
previously observed. Using simple arguments along with the consistency
requirements of an integrable theory, we find the exact elastic -matrix for
the quasiparticles scattering among themselves and off of the boundary. This
allows the calculation of the exact free energy, which agrees with the known
Bethe ansatz solution.Comment: 9 pages +1 figur