Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
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DOI：
10.1103/physrevb.102.201116
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发表时间：
2019-12
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通讯作者：
A. Nahum
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作者：
A. Nahum
我们提出了具有整体SO(4)对称性的二维SU(2)$_k$Wess-Zumino-Witten(WZW)理论通过将对称性扩大到SO$(4+\epsilon)$而继续到$2+\epsilon$维的可能性。这是由具有SO(5)对称性的三维Sigma模型和WZW项所推动的，WZW项与去受限临界有关。如果存在这样的连续性，重整化群流在小$\epsilon$处的结构可以通过假定在$\epsilon$中的解析性来固定。这导致了这样的猜想：WZW不动点在临界维度$dc>；2$处被一个新的、不稳定的不动点湮灭。对于所有的$k$，我们建议$d_c<；3$，并且我们在大的$k$的极限下计算$d_c$。这些流动支持SU(2)磁体中解禁闭相变是一个具有近似SO(5)的“伪临界”点的猜想，它受物理参数空间外的一个固定点控制。
We suggest the possibility that the two-dimensional SU(2)$_k$ Wess-Zumino-Witten (WZW) theory, which has global SO(4) symmetry, can be continued to $2+\epsilon$ dimensions by enlarging the symmetry to SO$(4+\epsilon)$. This is motivated by the three-dimensional sigma model with SO(5) symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $\epsilon$ may be fixed by assuming analyticity in $\epsilon$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality $d_c>2$. We suggest that $d_c < 3$ for all $k$, and we compute $d_c$ in the limit of large $k$. The flows support the conjecture that the deconfined phase transition in SU(2) magnets is a ``pseudocritical'' point with approximate SO(5), controlled by a fixed point slightly outside the physical parameter space.