613 research outputs found
Proof of the volume conjecture for Whitehead chains
We prove the volume conjecture for an infinite family of links called
Whitehead chains that generalizes both the Whitehead link and the Borromean
rings.Comment: 11 pages, 1 figure. See also
http://www.science.uva.nl/~riveen/papers.html New in version two is a
computation for the constant term in the asymptotic expansion. The proof of
lemma 5 has been omitted because it is almost the same as that of lemma
RG Domain Walls and Hybrid Triangulations
This paper studies the interplay between the N=2 gauge theories in three and
four dimensions that have a geometric description in terms of twisted
compactification of the six-dimensional (2,0) SCFT. Our main goal is to
construct the three-dimensional domain walls associated to any
three-dimensional cobordism. We find that we can build a variety of 3d theories
that represent the local degrees of freedom at a given domain wall in various
4d duality frames, including both UV S-dual frames and IR Seiberg-Witten
electric-magnetic dual frames. We pay special attention to Janus domain walls,
defined by four-dimensional Lagrangians with position-dependent couplings. If
the couplings on either side of the wall are weak in different UV duality
frames, Janus domain walls reduce to S-duality walls, i.e. domain walls that
encode the properties of UV dualities. If the couplings on one side are weak in
the IR and on the other weak in the UV, Janus domain walls reduce to RG walls,
i.e. domain walls that encode the properties of RG flows. We derive the 3d
geometries associated to both types of domain wall, and test their properties
in simple examples, both through basic field-theoretic considerations and via
comparison with quantum Teichmuller theory. Our main mathematical tool is a
parametrization and quantization of framed flat SL(K) connections on these
geometries based on ideal triangulations.Comment: 82+26 pages, 64 figure
Colored Jones polynomials without tails
We exhibit an infinite family of knots with the property that the first
coefficient of the n-colored Jones polynomial grows linearly with n. This shows
that the concept of stability and tail seen in the colored Jones polynomials of
alternating knots does not generalize naively.Comment: 5 pages, 1 ca
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