论文标题
三通四分之一模型
The tri-fundamental quartic model
论文作者
论文摘要
我们考虑具有短距离或远距离自由动作的多尺度场理论，以及在$ O（n_1）\ times o（n_2）\ times o（n_3）$变换下不变的四分之一相互作用，其标量字段形成了三符号的表示。我们研究了有限$ n $的两个循环的重新归一化组固定点，以及小$ε$的各种大$ n $缩放限制，后者是偏离关键维度的偏差或偏离自由传播器的关键缩放。特别是，对于同质情况，$ n_i = n $ for $ i = 1,2,3 $，我们研究了先前已知的固定点的跨座校正。在短程模型中，对于$εn^2 \ gg 1 $，我们发现具有非零四面体耦合的复杂固定点，在领先顺序下，arxiv的结果重现了：1707.03866;近代领先顺序的主要新颖性是关键指数获得了实际部分，从而可以正确识别某些固定点为IR稳定。在远程模型中，对于$εn\ ll 1 $，我们再次发现具有非零四面体耦合的复杂固定点，在领先顺序下，又重现了Arxiv的稳定固定点的线：1903.03578;在临近领先的顺序上，将其简化为离散的一组稳定固定点。短期和远距离案例之间的一个区别是，在前者中，关键指数纯粹是假想的，并在近代领先的顺序上获得了真正的部分，而在后者的情况下，情况却相反。
We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2) \times O(N_3)$ transformations, of which the scalar fields form a tri-fundamental representation. We study the renormalization group fixed points at two loops at finite $N$ and in various large-$N$ scaling limits for small $ε$, the latter being either the deviation from the critical dimension or from the critical scaling of the free propagator. In particular, for the homogeneous case $N_i = N$ for $i=1,2,3$, we study the subleading corrections to previously known fixed points. In the short-range model, for $εN^2\gg 1$, we find complex fixed points with non-zero tetrahedral coupling, that at leading order reproduce the results of arXiv:1707.03866 ; the main novelty at next-to-leading order is that the critical exponents acquire a real part, thus allowing a correct identification of some fixed points as IR stable. In the long-range model, for $εN \ll 1 $, we find again complex fixed points with non-zero tetrahedral coupling, that at leading order reproduce the line of stable fixed points of arXiv:1903.03578; at next-to-leading order, this is reduced to a discrete set of stable fixed points. One difference between the short-range and long-range cases is that, in the former the critical exponents are purely imaginary at leading-order and gain a real part at next-to-leading order, while for the latter the situation is reversed.
