Integrable and Conformal Boundary Conditions for ŝ l ( 2 ) A – D – E Lattice Models and Unitary Minimal Conformal Field Theories
Integrable and Conformal Boundary Conditions for ŝ l ( 2 ) A – D – E Lattice Models and Unitary Minimal Conformal Field Theories
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ŝ l ( 2 ) A – D – E 晶格模型和酉最小共形场论的可积和共形边界条件
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
P. Pearce
中科院分区：
文献类型：
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作者：
R. Behrend;P. Pearce
研究了统计力学的临界A-D-E模型和一般的基于图的格子模型的可积边界条件。特别地，利用与Temperley-Lieb代数和融合相关的技术，对于每个边界条件，得到了满足边界Yang-Baxter方程的边界Boltzmann权的集合。当适当地专门化时，这些边界权重(每个边界权重取决于三个自旋)分解为更自然的双自旋边缘权重。A-D-E情形的特殊边界条件与ŝL(2)酉极小共形场理论的共形边界条件自然一一对应。在这一点和进一步的证据的支持下，我们得出结论，在连续统标度极限下，可积边界条件提供了相应场论中完整的共形边界条件集的实现。
Integrable boundary conditions are studied for critical A–D–E and general graph-based lattice models of statistical mechanics. In particular, using techniques associated with the Temperley-Lieb algebra and fusion, a set of boundary Boltzmann weights which satisfies the boundary Yang-Baxter equation is obtained for each boundary condition. When appropriately specialized, these boundary weights, each of which depends on three spins, decompose into more natural two-spin edge weights. The specialized boundary conditions for the A–D–E cases are naturally in one-to-one correspondence with the conformal boundary conditions of ŝl(2) unitary minimal conformal field theories. Supported by this and further evidence, we conclude that, in the continuum scaling limit, the integrable boundary conditions provide realizations of the complete set of conformal boundary conditions in the corresponding field theories.