3,530 research outputs found
Chern-Simons Theory, Colored-Oriented Braids and Link invariants
A method to obtain explicit and complete topological solution of SU(2)
Chern-Simons theory on is developed. To this effect the necessary aspects
of the theory of coloured-oriented braids and duality properties of conformal
blocks for the correlators of Wess-Zumino conformal field theory are
presented. A large class of representations of the generators of the groupoid
of coloured-oriented braids are obtained. These provide a whole lot of new link
invariants of which Jones polynomials are the simplest examples. These new
invariants are explicitly calculated as illustrations for knots upto eight
crossings and two-component multicoloured links upto seven crossings.Comment: 48 pages + 20 diagram
Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole
We derive an exact expression for the partition function of the Euclidean BTZ
black hole. Using this, we show that for a black hole with large horizon area,
the correction to the Bekenstein-Hawking entropy is , in
agreement with that for the Schwarzschild black hole obtained in the canonical
gravity formalism and also in a Lorentzian computation of BTZ black hole
entropy. We find that the right expression for the logarithmic correction in
the context of the BTZ black hole comes from the modular invariance associated
with the toral boundary of the black hole.Comment: LaTeX, 10 pages, typos corrected, clarifications adde
Chirality of Knots and and Chern-Simons Theory
Upto ten crossing number, there are two knots, and whose
chirality is not detected by any of the known polynomials, namely, Jones
invariants and their two variable generalisations, HOMFLY and Kauffman
invariants. We show that the generalised knot invariants, obtained through
Chern-Simons topological field theory, which give the known polynomials
as special cases, are indeed sensitive to the chirality of these knots.Comment: 15 pages + 7 diagrams (available on request
Representations of Composite Braids and Invariants for Mutant Knots and Links in Chern-Simons Field Theories
We show that any of the new knot invariants obtained from Chern-Simons theory
based on an arbitrary non-abelian gauge group do not distinguish isotopically
inequivalent mutant knots and links. In an attempt to distinguish these knots
and links, we study Murakami (symmetrized version) -strand composite braids.
Salient features of the theory of such composite braids are presented.
Representations of generators for these braids are obtained by exploiting
properties of Hilbert spaces associated with the correlators of Wess-Zumino
conformal field theories. The -composite invariants for the knots are given
by the sum of elementary Chern-Simons invariants associated with the
irreducible representations in the product of representations (allowed by
the fusion rules of the corresponding Wess-Zumino conformal field theory)
placed on the individual strands of the composite braid. On the other hand,
composite invariants for links are given by a weighted sum of elementary
multicoloured Chern-Simons invariants. Some mutant links can be distinguished
through the composite invariants, but mutant knots do not share this property.
The results, though developed in detail within the framework of
Chern-Simons theory are valid for any other non-abelian gauge group.Comment: Latex, 25pages + 16 diagrams available on reques
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