Conformal Field Theory / Théorie des champs conformes
(Org: Terry Gannon and/et Mark Walton)
- C. CUMMINS, Concordia University, Montreal, Quebec
In recent years modular invariance has been recognised as playing an
important role in many areas of mathematics and physics. In this talk I
shall discuss the computation and classification of congruence
subgroups of groups commensurable with the modular group. Part of the
aim of this project is to find a complete list of low genus subgroups
and in particular a listing of all Hauptmoduls ( which arise, for
example, in the study of moonshine).
- MARC DE MONTIGNY, Alberta
- BENJAMIN DOYON, Department of Physics, Rutgers University, Piscataway,
New Jersey 08854, USA
Twisted modules for vertex operator algebras and
In this work, joint with J. Lepowsky and A. Milas, we describe how,
using general principles of the theory of vertex operator algebras and
their twisted modules, one can obtain a bosonic, twisted construction
of a certain central extension of a Lie algebra of differential
operators on the circle, for an arbitrary twisting automorphism. The
construction involves the Bernoulli polynomials in a fundamental way.
This is explained through results in the general theory of vertex
operator algebras, including a new identity, which we call "modified
- T. GANNON, University of Alberta, Edmonton
The classification of fusion rings, I
In this introductory talk I will define from first principles the
concepts of fusion rings and modular data, which play fundamental roles
in e.g. conformal field theory. I will run over the basic examples and
their elementary properties. Very little is known in the literature
regarding their classification, and this is a glaring open problem.
I'll review what is known, and describe the methods those researchers
used. Then I'll introduce the new methods which we (my collaborator
Mark Jackson and I) believe will permit considerable further progress.
In his talk ("The classification of fusion rings, II"), Jackson will
describe the results we have obtained thus far.
- J. GEGENBERG, New Brunswick
- MARK JACKSON, University of Alberta
The classification of fusion rings, II
Although many examples of fusion rings and modular data do exist(e.g.
those arising from Kac-Moody algebras and finite groups) a
classification, except in dimensions up to 3, has yet to completed.
In an earlier talk ("The classification of fusion rings, I"), my
collaborator Terry Gannon sketched our new approach to attacking this
fundamental problem. In this talk I will describe our results. In
particular, I will illustrate our approach with a proof that classifies
3 dimensional fusion rings which is considerably shorter and more
transparent than any appearing in the literature. Early results for
dimensions 4 and 5 will also be presented.
- J. LEPOWSKY, Rutgers University, Piscataway, New Jersey 08854-8019, USA
Intertwining operators for vertex operator algebras and
recursions for q-series
Vertex operator constructions of affine Lie algebras and
"Z-algebras" have been used to prove, interpret or conjecture many
interesting combinatorial partition identities, including the classical
Rogers-Ramanujan identities. More recently, Feigin and Stoyanovsky have
interpreted certain such combinatorial identities in terms of what they
call the "principal subspaces" of certain modules. One of the
classical methods for studying such identities is the
"Rogers-Ramanujan recursion" for certain formal power series, and
generalizations of this recursion discovered by Rogers and Selberg. In
the present work, joint with S. Capparelli and A. Milas, we introduce
such recursions into the theory of vertex operator algebras by
recovering them by means of the theory of intertwining operators for
modules for vertex operator algebras.
- R. MANN, University of Waterloo, Waterloo, Ontario N2L 3G1
From soup to NUTS
Studies of black hole pair production in the cosmic soup of the early
universe provided the first suggestive hints that de Sitter spacetime
had maximal entropy. Insights from Holographic and the (A)dS/CFT
correspondence later resulted in a formalization of this notion into
the N-bound conjecture, which states that that any spacetime with
positive cosmological constant L = 3l-2 has observable
entropy S £ SdS=pl2. From this followed the notion
that dS spacetime also had maximal mass/energy, expressed in the form
of a conjecture that any asymptotically dS spacetime with mass greater
than pure dS has a cosmological singularity.
Asymptotically dS spacetimes with NUT charge, however, provide
counterexamples to these conjectures under certain circumstances. Such
spacetimes can have a mass greater than dS spacetime whilst respecting
the N-bound on entropy, and can also violate the N-bound in certain
circumstances. I shall discuss the basic geometric structure of
NUT-charged dS spacetimes, illustrating by example how such violations
occur, and discuss the implications for holography.
- P. MATHIEU, Laval
- J. RASMUSSEN, CRM, Universite de Montreal, Montreal, Quebec
On the su(2)-1/2 WZW model
The bosonic bg ghost system is equivalent to an
su(2)-1/2 WZW model, and is found to have an infinite number of
representations with increasingly negative dimensions. This
contradicts the traditional belief (based on the Kac-Wakimoto
characters) that the four admissible representations are the only ones
present. To facilitate computations, a faithful free-field
representation is available. It may be extended by extra zero modes,
allowing lifts of the model. These new models contain so-called
relaxed representations. Indecomposable representations are also
encountered, reflecting that the associated lifted model is a
logarithmic CFT. Modular invariance will be addressed briefly.
- GORDON SEMENOFF, UBC
- M. WALTON, University of Lethbridge, Lethbridge, Alberta T1K 3M4
The fusion of the Wess-Zumino-Novikov-Witten conformal field theories
is associated with their chiral algebras, the nontwisted affine
Kac-Moody algebras. Properties of this affine fusion will be reviewed.
Results and conjectures from the mathematical physics literature will