Kazakov Vladimir, Sobko Evgeny, Zarembo Konstantin
Laboratoire de physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France and Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland.
School of Physics and Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.
Phys Rev Lett. 2020 May 15;124(19):191602. doi: 10.1103/PhysRevLett.124.191602.
We initiate a systematic, non-perturbative study of the large-N expansion in the two-dimensional SU(N)×SU(N) principal Chiral model (PCM). Starting with the known infinite-N solution for the ground state at fixed chemical potential, we devise an iterative procedure to solve the Bethe ansatz equations order by order in 1/N. The first few orders, which we explicitly compute, reveal a systematic enhancement pattern at strong coupling calling for the near-threshold resummation of the large-N expansion. The resulting double-scaling limit bears striking similarities to the c=1 noncritical string theory and suggests that the double-scaled PCM is dual to a noncritical string with a (2+1)-dimensional target space where an additional dimension emerges dynamically from the SU(N) Dynkin diagram.
我们对二维SU(N)×SU(N)主手征模型（PCM）中的大N展开进行了系统的、非微扰的研究。从固定化学势下基态的已知无穷N解出发，我们设计了一种迭代程序，以逐阶求解1/N下的贝塞耳假设方程。我们明确计算的前几阶揭示了强耦合下的一种系统增强模式，这需要对大N展开进行近阈值重求和。由此得到的双标度极限与c = 1非临界弦理论有着显著的相似性，并表明双标度PCM与具有(2 + 1)维目标空间的非临界弦对偶，其中一个额外维度从SU(N) Dynkin图动态出现。
