90 research outputs found
Boundary Conformal Field Theories, Limit Sets of Kleinian Groups and Holography
In this paper,based on the available mathematical works on geometry and
topology of hyperbolic manifolds and discrete groups, some results of Freedman
et al (hep-th/9804058) are reproduced and broadly generalized. Among many new
results the possibility of extension of work of Belavin, Polyakov and
Zamolodchikov to higher dimensions is investigated. Known in physical
literature objections against such extension are removed and the possibility of
an extension is convincingly demonstrated.Comment: 62 pages, 5 figure
On continuous extension of grafting maps
The definition of the grafting operation for quasifuchsian groups is extended
by Bromberg to all -groups. Although the grafting maps are not necessarily
continuous at boundary groups, in this paper, we show that the grafting maps
take every "standard" convergent sequence to a convergent sequence. As a
consequence of this result, we extend Goldman's grafting theorem for
quasifuchsian groups to all boundary -groups.Comment: 24 pages, 2 figure
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