作为高阶非酉最小陪集的融合RSOS格模型
Fused RSOS Lattice Models as Higher-Level Nonunitary Minimal Cosets
摘要：
我们考虑了具有交叉参数$λ=(m'\!-\!m)π/m'$的Forrester-Baxter RSOS格点模型。在连续标度极限下，这些模型由最小模型${\cal M}(m,m')$描述。我们推测，对于$λ<π/n$，$n\times n$融合的RSOS模型与$n\ge 2$是由更高级别的陪集$(A^{(1)}_1)_k\otimes (A^{(1)}_1)_n/(A^{(1)}_1)_{k+n}$描述的分数级$k=nM/(M'\!-\!M)-2$与$(M,M')=\big(nm-(n\!-\!1)m',m'\big)$。为了支持这一猜想，我们调查所产生的巴克斯特的非临界角转移矩阵的一维总和。在酉情形（$m=m'\!-\!1$）中，已知直到$q$的前导幂，这些与分支函数$b_{r,s,\ell}^{m'\!-n,m'\!,n}(q)$一致。对于一般非幺正的情况下（$m<m'\!-\!1$），我们确定的基态一维RSOS路径，并将它们与量子数$(r,s,\ell)$在各个部门。对于$n=1,2,3$，我们得到了当地的能量函数$H(a,b,c)$在一个合适的规范和验证，相关的一维和产生的有限形式收敛，$N$变得大，分数级分支函数$b_{r,s,\ell}^{M,M'\!,n}(q)$。扩展Schilling的工作，我们还猜想有限玻色子分支函数$b_{r,s,\ell}^{M,M'\!,n;(N)}(q)$一般$n$和检查，这些同意与一维总和$n=1,2,3$系统大小$N=14$。最后，将{ \em对数极限\/} $m,m'\to\infty$与$m/m'\to p/p'+$取和，得到了$n\times n$融合对数极小模型${\cal LM}(p,p')$的有限化Kac特征$χ_{r,s,\ell}^{P,P'\!,n;(N)}(q)$.
英文摘要：
We consider the Forrester-Baxter RSOS lattice models with crossing parameter $λ=(m'\!-\!m)π/m'$ in Regime~III. In the continuum scaling limit, these models are described by the minimal models ${\cal M}(m,m')$. We conjecture that, for $λ<π/n$, the $n\times n$ fused RSOS models with $n\ge 2$ are described by the higher-level coset $(A^{(1)}_1)_k\otimes (A^{(1)}_1)_n/(A^{(1)}_1)_{k+n}$ at fractional level $k=nM/(M'\!-\!M)-2$ with $(M,M')=\big(nm-(n\!-\!1)m',m'\big)$. To support this conjecture, we investigate the one-dimensional sums arising from Baxter's off-critical corner transfer matrices. In unitary cases ($m=m'\!-\!1$) it is known that, up to leading powers of $q$, these coincide with the branching functions $b_{r,s,\ell}^{m'\!-n,m'\!,n}(q)$. For general nonunitary cases ($m<m'\!-\!1$), we identify the ground state one-dimensional RSOS paths and relate them to the quantum numbers $(r,s,\ell)$ in the various sectors. For $n=1,2,3$, we obtain the local energy functions $H(a,b,c)$ in a suitable gauge and verify that the associated one-dimensional sums produce finitized forms that converge, as $N$ becomes large, to the fractional level branching functions $b_{r,s,\ell}^{M,M'\!,n}(q)$. Extending the work of Schilling, we also conjecture finitized bosonic branching functions $b_{r,s,\ell}^{M,M'\!,n;(N)}(q)$ for general $n$ and check that these agree with the one-dimensional sums for $n=1,2,3$ out to system sizes $N=14$. Lastly, the finitized Kac characters $χ_{r,s,\ell}^{P,P'\!,n;(N)}(q)$ of the $n\times n$ fused logarithmic minimal models ${\cal LM}(p,p')$ are obtained by taking the {\em logarithmic limit\/} $m,m'\to\infty$ with $m/m'\to p/p'+$.
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