3,232 research outputs found
On Dubrovin Topological Field Theories
I show that the new topological field theories recently associated by
Dubrovin with each Coxeter group may be all obtained in a simple way by a
``restriction'' of the standard ADE solutions. I then study the Chebichev
specializations of these topological algebras, examine how the Coxeter graphs
and matrices reappear in the dual algebra and mention the intriguing connection
with the operator product algebra of conformal field theories. A direct
understanding of the occurrence of Coxeter groups in that context is highly
desirable.Comment: 15 page
Generalised twisted partition functions
We consider the set of partition functions that result from the insertion of
twist operators compatible with conformal invariance in a given 2D Conformal
Field Theory (CFT). A consistency equation, which gives a classification of
twists, is written and solved in particular cases. This generalises old results
on twisted torus boundary conditions, gives a physical interpretation of
Ocneanu's algebraic construction, and might offer a new route to the study of
properties of CFT.Comment: 12 pages, harvmac, 1 Table, 1 Figure . Minor typos corrected, the
figure which had vanished reappears
Conformal Boundary Conditions and what they teach us
The question of boundary conditions in conformal field theories is discussed,
in the light of recent progress. Two kinds of boundary conditions are examined,
along open boundaries of the system, or along closed curves or ``seams''.
Solving consistency conditions known as Cardy equation is shown to amount to
the algebraic problem of finding integer valued representations of (one or two
copies of) the fusion algebra. Graphs encode these boundary conditions in a
natural way, but are also relevant in several aspects of physics ``in the
bulk''. Quantum algebras attached to these graphs contain information on
structure constants of the operator algebra, on the Boltzmann weights of the
corresponding integrable lattice models etc. Thus the study of boundary
conditions in Conformal Field Theory offers a new perspective on several old
physical problems and offers an explicit realisation of recent mathematical
concepts.Comment: Expanded version of lectures given at the Summer School and
Conference Nonperturbative Quantum Field Theoretic Methods and their
Applications, August 2000, Budapest, Hungary. 35 page
Knot theory and matrix integrals
The large size limit of matrix integrals with quartic potential may be used
to count alternating links and tangles. The removal of redundancies amounts to
renormalizations of the potential. This extends into two directions: higher
genus and the counting of "virtual" links and tangles; and the counting of
"coloured" alternating links and tangles. We discuss the asymptotic behavior of
the number of tangles as the number of crossings goes to infinity.Comment: chapter of the book Random Matrix Theory, Eds Akemann, Baik and Di
Francesc
Justifying Social Discounting: The Rank-Discounted Utilitarian Approach
The discounted utilitarian criterion for infinite horizon social choice has been criticized for treating generations unequally. We propose an extended rank-discounted utilitarian (ERDU) criterion instead. The criterion amounts to discounted utilitarianism on non-decreasing streams, but it treats all generations impartially: discounting becomes the mere expression of intergenerational inequality aversion. We show that more inequality averse ERDU societies have higher social discount rates when future generations are better-off. We apply the ERDU approach in two benchmark economic growth models and prove that it promotes sustainable policies that maximize discounted utilitarian welfare.intergenerational equity, social discounting, discounted utilitarianism, sustainability
- âŠ