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arXiv 1003.5282hep-th
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复合不变量与无向拓扑弦振幅

Composite Invariants and Unoriented Topological String Amplitudes

Chandrima Paul, Pravina Borhade, P. Ramadevi

摘要:

Sinha和Vafa证明了在$S^3$上的$SO$ Chern-Simons规范理论必须与在分解锥的定向折叠上的闭$A$ -模型拓扑弦对偶。虽然Chern-Simons自由能可以重写的拓扑弦振幅提供证据的猜想,我们需要一个新的想法,在威尔逊圈的背景下,观察到提取交叉帽$c=0,1,2$拓扑振幅。Marino在Morton和Ryder工作的基础上发表的最新论文清楚地表明,放置在节点和链接上的复合表示对重写拓扑弦交叉帽$c=0$振幅起着至关重要的作用。这使得能够提取未定向的交叉帽$c=2$拓扑幅度。本文明确地给出了U(N)Chern-Simons理论中带有复合表示的框架纽结和环的复合不变量。我们验证了广义鲁道夫定理,该定理将复合不变量与SO(N)Chern-Simons理论中的不变量联系起来,并且还验证了Marino关于拓扑弦振幅的完整性性质的猜想。对于某些框架纽结和链环,我们已经将交叉帽$c=0$、$c=1$和$c=2$的BPS整数不变量制成表格,给出了解析锥的定向折叠上的开弦拓扑振幅。

英文摘要:

Sinha and Vafa 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 based on the work of Morton and Ryder 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 $c=0$, $c=1$ and $c=2$ giving the open-string topological amplitude on the orientifold of the resolved conifold.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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