Sorbonne Universités, UPMC Université Paris 6, UMR 7589, LPTHE, F-75005 Paris, France.
CNRS, UMR 7589, LPTHE, F-75005 Paris, France.
Phys Rev Lett. 2016 Apr 1;116(13):130601. doi: 10.1103/PhysRevLett.116.130601. Epub 2016 Mar 29.
The possibility of extending the Liouville conformal field theory from values of the central charge c≥25 to c≤1 has been debated for many years in condensed matter physics as well as in string theory. It was only recently proven that such an extension-involving a real spectrum of critical exponents as well as an analytic continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov formula for three-point couplings-does give rise to a consistent theory. We show in this Letter that this theory can be interpreted in terms of microscopic loop models. We introduce in particular a family of geometrical operators, and, using an efficient algorithm to compute three-point functions from the lattice, we show that their operator algebra corresponds exactly to that of vertex operators V_{α[over ^]} in c≤1 Liouville theory. We interpret geometrically the limit α[over ^]→0 of V_{α[over ^]} and explain why it is not the identity operator (despite having conformal weight Δ=0).
多年来，凝聚态物理和弦理论一直在争论是否可以将刘维尔共形场论从中心荷 c≥25 扩展到 c≤1。直到最近才证明，这种扩展——涉及临界指数的实谱以及 Dorn-Otto-Zamolodchikov-Zamolodchikov 三点耦合公式的解析延拓——确实会产生一致的理论。在这封信中，我们表明，该理论可以用微观环模型来解释。我们特别引入了一类几何算子，并使用一种有效的算法从格点上计算三点函数，结果表明它们的算子代数与 c≤1 刘维尔理论中顶点算子 V_{α[over ^]}的算子代数完全一致。我们从几何上解释了 V_{α[over ^]}的极限 α[over ^]→0，并解释了为什么它不是恒等算子（尽管具有共形权 Δ=0）。
