Title: The continuum limit of $a_{N-1}^{(2)}$ spin chains Show Chinese title

Title: 自旋链的连续极限$a_{N-1}^{(2)}$

Abstract: Building on our previous work for $a_2^{(2)}$ and $a_3^{(2)}$ we explore systematically the continuum limit of gapless $a_{N-1}^{(2)}$ vertex models and spin chains. We find the existence of three possible regimes. Regimes I and II for $a_{2n-1}^{(2)}$ are related with $a_{2n-1}^{(2)}$ Toda, and described by $n$ compact bosons. Regime I for $a_{2n}^{(2)}$ is related with $a_{2n}^{(2)}$ Toda and involves $n$ compact bosons, while regime II is related instead with $B^{(1)}(0,n)$ super Toda, and involves in addition a single Majorana fermion. The most interesting is regime III, where {\sl non-compact} degrees of freedom appear, generalising the emergence of the Euclidean black hole CFT in the $a_{2}^{(2)}$ case. For $a_{2n}^{(2)}$ we find a continuum limit made of $n$ compact and $n$ non-compact bosons, while for $a_{2n-1}^{(2)}$ we find $n$ compact and $n-1$ non-compact bosons. We also find deep relations between $a_{N-1}^{(2)}$ in regime III and the gauged WZW models $SO(N)/SO(N-1)$. Show Chinese abstract

Abstract: 基于我们之前关于$a_2^{(2)}$和$a_3^{(2)}$的工作，我们系统地探讨了无能隙$a_{N-1}^{(2)}$顶点模型和自旋链的连续极限。我们发现存在三种可能的区域。对于$a_{2n-1}^{(2)}$，区域 I 和 II 与$a_{2n-1}^{(2)}$拓扑相关，并由$n$紧致玻色子描述。 I区与$a_{2n}^{(2)}$有关，并涉及$a_{2n}^{(2)}$和$n$的紧致玻色子，而II区则与$B^{(1)}(0,n)$超Toda相关，同时还涉及一个马约拉纳费米子。 最有趣的是III区，在此区域出现{\sl 非紧致}自由度，推广了$a_{2}^{(2)}$情况下欧几里得黑洞CFT的出现。 对于$a_{2n}^{(2)}$，我们找到一个由$n$个紧致和$n$个非紧致玻色子组成的连续极限，而对于$a_{2n-1}^{(2)}$，我们找到$n$个紧致和$n-1$个非紧致玻色子。 我们还发现第三区域中的 $a_{N-1}^{(2)}$ 与规范化的WZW模型 $SO(N)/SO(N-1)$之间存在深刻的联系。