427 research outputs found
A Trinomial Analogue of Bailey's Lemma and N=2 Superconformal Invariance
We propose and prove a trinomial version of the celebrated Bailey's lemma. As
an application we obtain new fermionic representations for characters of some
unitary as well as nonunitary models of N = 2 superconformal field theory
(SCFT). We also establish interesting relations between N = 1 and N = 2 models
of SCFT with central charges and . A number of new mock theta function identities are derived.Comment: Reference and note adde
A new four parameter q-series identity and its partition implications
We prove a new four parameter q-hypergeometric series identity from which the
three parameter key identity for the Goellnitz theorem due to Alladi, Andrews,
and Gordon, follows as a special case by setting one of the parameters equal to
0. The new identity is equivalent to a four parameter partition theorem which
extends the deep theorem of Goellnitz and thereby settles a problem raised by
Andrews thirty years ago. Some consequences including a quadruple product
extension of Jacobi's triple product identity, and prospects of future research
are briefly discussed.Comment: 25 pages, in Sec. 3 Table 1 is added, discussion is added at the end
of Sec. 5, minor stylistic changes, typos eliminated. To appear in
Inventiones Mathematica
Supersymmetric pairing of kinks for polynomial nonlinearities
We show how one can obtain kink solutions of ordinary differential equations
with polynomial nonlinearities by an efficient factorization procedure directly
related to the factorization of their nonlinear polynomial part. We focus on
reaction-diffusion equations in the travelling frame and
damped-anharmonic-oscillator equations. We also report an interesting pairing
of the kink solutions, a result obtained by reversing the factorization
brackets in the supersymmetric quantum mechanical style. In this way, one gets
ordinary differential equations with a different polynomial nonlinearity
possessing kink solutions of different width but propagating at the same
velocity as the kinks of the original equation. This pairing of kinks could
have many applications. We illustrate the mathematical procedure with several
important cases, among which the generalized Fisher equation, the
FitzHugh-Nagumo equation, and the polymerization fronts of microtubulesComment: 13 pages, 2 figures, revised during the 2nd week of Dec. 200
Central Charge and the Andrews-Bailey Construction
From the equivalence of the bosonic and fermionic representations of
finitized characters in conformal field theory, one can extract mathematical
objects known as Bailey pairs. Recently Berkovich, McCoy and Schilling have
constructed a `generalized' character formula depending on two parameters \ra
and , using the Bailey pairs of the unitary model . By taking
appropriate limits of these parameters, they were able to obtain the characters
of model , model , and the unitary model with
central charge . In this letter we computed the effective
central charge associated with this `generalized' character formula using a
saddle point method. The result is a simple expression in dilogarithms which
interpolates between the central charges of these unitary models.Comment: Latex2e, requires cite.sty package, 13 pages. Additional footnote,
citation and reference
Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)
In this paper, we formulate the geometric Bogomolov conjecture for abelian
varieties, and give some partial answers to it. In fact, we insist in a main
theorem that under some degeneracy condition, a closed subvariety of an abelian
variety does not have a dense subset of small points if it is a non-special
subvariety. The key of the proof is the study of the minimal dimension of the
components of a canonical measure on the tropicalization of the closed
subvariety. Then we can apply the tropical version of equidistribution theory
due to Gubler. This article includes an appendix by Walter Gubler. He shows
that the minimal dimension of the components of a canonical measure is equal to
the dimension of the abelian part of the subvariety. We can apply this result
to make a further contribution to the geometric Bogomolov conjecture.Comment: 30 page
Quantum Clifford-Hopf Algebras for Even Dimensions
In this paper we study the quantum Clifford-Hopf algebras
for even dimensions and obtain their intertwiner matrices, which are
elliptic solutions to the Yang- Baxter equation. In the trigonometric limit of
these new algebras we find the possibility to connect with extended
supersymmetry. We also analyze the corresponding spin chain hamiltonian, which
leads to Suzuki's generalized model.Comment: 12 pages, LaTeX, IMAFF-12/93 (final version to be published, 2
uuencoded figures added
Parafermion statistics and the application to non-abelian quantum Hall states
The (exclusion) statistics of parafermions is used to study degeneracies of
quasiholes over the paired (or in general clustered) quantum Hall states. Focus
is on the Z_k and su(3)_k/u(1)^2 parafermions, which are used in the
description of spin-polarized and spin-singled clustered quantum Hall states.Comment: 15 pages, minor changes, as publishe
Infrared Behaviour of Massless Integrable Flows entering the Minimal Models from phi_31
It is known that any minimal model M_p receives along its phi_31 irrelevant
direction *two* massless integrable flows: one from M_{p+1} perturbed by
phi_{13}, the other from Z_{p-1} parafermionic model perturbed by its
generating parafermion field. By comparing Thermodynamic Bethe Ansatz data and
``predictions'' of infrared Conformal Perturbation Theory we show that these
two flows are received by M_p with opposite coupling constants of the phi_31
irrelevant perturbation. Some comments on the massless S matrices of these two
flows are added.Comment: 12 pages, Latex - One misprinted (uninfluent) coefficient corrected
in Tab.
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