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Composite representation invariants and unoriented topological string amplitudes

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Title Composite representation invariants and unoriented topological string amplitudes
 
Creator PAUL, C
BORHADE, P
RAMADEVI, P
 
Subject link invariants
 
Description Sinha and Vafa [1] had conjectured that the SO Chern-Simons gauge theory on S(3) must be dual to the closed A-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be rewritten in terms of the topological string amplitudes providing evidence for the conjecture, we needed a novel idea in the context of Wilson loop observables to extract cross-cap c = 0, 1, 2 topological amplitudes. Recent paper of Marino [2] based on the work of Morton and Ryder [3] has clearly shown that the composite representation placed on the knots and links plays a crucial role to rewrite the topological string cross-cap c = 0 amplitude. This enables extracting the unoriented cross-cap c = 2 topological amplitude. In this paper, we have explicitly worked out the composite invariants for some framed knots and links carrying composite representations in U(N) Chern-Simons theory. We have verified generalised Rudolph's theorem, which relates composite invariants to the invariants in SO(N) Chern-Simons theory, and also verified Marino's conjectures on the integrality properties of the topological string amplitudes. For some framed knots and links, we have tabulated the BPS integer invariants for cross-cap c = 0 and c = 2 giving the open-string topological amplitude on the orientifold of the resolved conifold. .
 
Publisher ELSEVIER SCIENCE BV
 
Date 2011-07-24T14:11:22Z
2011-12-26T12:57:13Z
2011-12-27T05:47:10Z
2011-07-24T14:11:22Z
2011-12-26T12:57:13Z
2011-12-27T05:47:10Z
2010
 
Type Article
 
Identifier NUCLEAR PHYSICS B, 841(3), 448-462
0550-3213
http://dx.doi.org/10.1016/j.nuclphysb.2010.08.013
http://dspace.library.iitb.ac.in/xmlui/handle/10054/6446
http://hdl.handle.net/10054/6446
 
Language en