3,080 research outputs found
Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
We define the chiral zero modes' phase space of the G=SU(n)
Wess-Zumino-Novikov-Witten model as an (n-1)(n+2)-dimensional manifold M_q
equipped with a symplectic form involving a special 2-form - the Wess-Zumino
(WZ) term - which depends on the monodromy M. This classical system exhibits a
Poisson-Lie symmetry that evolves upon quantization into an U_q(sl_n) symmetry
for q a primitive even root of 1. For each constant solution of the classical
Yang-Baxter equation we write down explicitly a corresponding WZ term and
invert the symplectic form thus computing the Poisson bivector of the system.
The resulting Poisson brackets appear as the classical counterpart of the
exchange relations of the quantum matrix algebra studied previously. We argue
that it is advantageous to equate the determinant D of the zero modes' matrix
to a pseudoinvariant under permutations q-polynomial in the SU(n) weights,
rather than to adopt the familiar convention D=1.Comment: 30 pages, LaTeX, uses amsfonts; v.2 - small corrections, Appendix and
a reference added; v.3 - amended version for J. Phys.
A Unified Conformal Field Theory Description of Paired Quantum Hall States
The wave functions of the Haldane-Rezayi paired Hall state have been
previously described by a non-unitary conformal field theory with central
charge c=-2. Moreover, a relation with the c=1 unitary Weyl fermion has been
suggested. We construct the complete unitary theory and show that it
consistently describes the edge excitations of the Haldane-Rezayi state.
Actually, we show that the unitary (c=1) and non-unitary (c=-2) theories are
related by a local map between the two sets of fields and by a suitable change
of conjugation. The unitary theory of the Haldane-Rezayi state is found to be
the same as that of the 331 paired Hall state. Furthermore, the analysis of
modular invariant partition functions shows that no alternative unitary
descriptions are possible for the Haldane-Rezayi state within the class of
rational conformal field theories with abelian current algebra. Finally, the
known c=3/2 conformal theory of the Pfaffian state is also obtained from the
331 theory by a reduction of degrees of freedom which can be physically
realized in the double-layer Hall systems.Comment: Latex, 42 pages, 2 figures, 3 tables; minor corrections to text and
reference
On the classifications of unitary lowest weight representations of conformal current algebras
-cluster categories and -replicated algebras
Let A be a hereditary algebra over an algebraically closed field. We prove
that an exact fundamental domain for the m-cluster category of A is the m-left
part of the m-replicated algebra of A. Moreover, we obtain a
one-to-one correspondence between the tilting objects in the m-cluster category
(that is, the m-clusters) and those tilting -modules for which all non
projective-injective direct summands lie in the m-left part of .Comment: 28 pages, 2 figure
About the magnetic fluctuation effect on the phase transition to superconducting state in Al
The free energy and the order parameter profile near the phase transition to
the superconducting state in bulk Al samples are calculated within a
mean-field-like approximation. The results are compared with those for thin
films.Comment: 11 pages, miktex, 2 figure
Asymptotically free four-fermion interactions and electroweak symmetry breaking
We investigate the fermions of the standard model without a Higgs scalar.
Instead, we consider a non-local four-quark interaction in the tensor channel
which is characterized by a single dimensionless coupling . Quantization
leads to a consistent perturbative expansion for small . The running of
is asymptotically free and therefore induces a non-perturbative scale
, in analogy to the strong interactions. We argue that
spontaneous electroweak symmetry breaking is triggered at a scale where
grows large and find the top quark mass of the order of . We also
present a first estimate of the effective Yukawa coupling of a composite Higgs
scalar to the top quark, as well as the associated mass ratio between the top
quark and the W boson.Comment: 24 page
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