|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'585
Articles rated: 2609
24 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Knot Homology from Refined Chern-Simons Theory | | Mina Aganagic
; Shamil Shakirov
; | | Date: |
25 May 2011 | | Abstract: | We formulate a refinement of SU(N) Chern-Simons theory on a three-manifold
via the refined topological string and the (2,0) theory on N M5 branes. The
refined Chern-Simons theory is defined on any three-manifold with a semi-free
circle action. We give an explicit solution of the theory, in terms of a
one-parameter refinement of the S and T matrices of Chern-Simons theory,
related to the theory of Macdonald polynomials. The ordinary and refined
Chern-Simons theory are similar in many ways; for example, the Verlinde formula
holds in both. We obtain new topological invariants of Seifert three-manifolds
and torus knots inside them. We conjecture that the knot invariants we compute
are the Poincare polynomials of the sl(n) knot homology theory. The latter
includes the Khovanov-Rozansky knot homology, as a special case. The conjecture
passes a number of nontrivial checks. We show that, for a large number of torus
knots colored with the fundamental representation of SU(N), our knot invariants
agree with the Poincare polynomials of Khovanov-Rozansky homology. As a
byproduct, we show that our theory on S^3 has a large-N dual which is the
refined topological string on X=O(-1)+O(-1)->P^1; this supports the conjecture
by Gukov, Schwarz and Vafa relating the spectrum of BPS states on X to sl(n)
knot homology. We also provide a matrix model description of some amplitudes of
the refined Chern-Simons theory on S^3. | | Source: | arXiv, 1105.5117 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER