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arXiv 0804.4335hep-th
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临界渗流的W-扩展融合代数

W-Extended Fusion Algebra of Critical Percolation

Jorgen Rasmussen, Paul A. Pearce

备注：
30 pages
发表信息：
J.Phys.A41:295208,2008
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摘要：

二维临界渗流是Yang-Baxter可积对数极小模型LM（p，p '）无穷级数的成员LM（2，3）。我们认为这个晶格模型的连续标度极限作为一个“合理的”对数共形场论与扩展W= W_{2,3}对称性，并使用一个带上的晶格方法来研究基本的融合规则，在这个扩展的图片。我们发现，随后的闭融合代数的表示内容包含26个W-不可分解表示，其中8个秩1表示，14个秩2表示和4个秩3表示。我们确定这些表示与适当的限制Yang-Baxter可积边界条件的格，并获得其相关的W-扩展字符。后者分解为W-不可约字符的有限非负和，其中需要13个。在格上实现融合，使我们能够读出的融合规则管理的融合代数的26个表示，并构造一个明确的凯莱表。这些表象在融合中相互封闭，这是对所提出的扩展对称性的显著证实。

英文摘要：

Two-dimensional critical percolation is the member LM(2,3) of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We consider the continuum scaling limit of this lattice model as a `rational' logarithmic conformal field theory with extended W=W_{2,3} symmetry and use a lattice approach on a strip to study the fundamental fusion rules in this extended picture. We find that the representation content of the ensuing closed fusion algebra contains 26 W-indecomposable representations with 8 rank-1 representations, 14 rank-2 representations and 4 rank-3 representations. We identify these representations with suitable limits of Yang-Baxter integrable boundary conditions on the lattice and obtain their associated W-extended characters. The latter decompose as finite non-negative sums of W-irreducible characters of which 13 are required. Implementation of fusion on the lattice allows us to read off the fusion rules governing the fusion algebra of the 26 representations and to construct an explicit Cayley table. The closure of these representations among themselves under fusion is remarkable confirmation of the proposed extended symmetry.

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