论文标题
关于Hermitian多矩阵模型的大型$ d $扩展
On the large $D$ expansion of Hermitian multi-matrix models
论文作者
论文摘要
我们调查了$ 1/n^{2} $的双重渐近扩展的存在和属性，$ 1/\ sqrt {d} $中的$ \ Mathrm {u}（n）\ times \ times \ mathrm {o}（o}（o}（o）） $ \ mathrm {o}（d）$。关键点是证明上限$η（h）$在最大功率$ d^{1+η（h）} $ $ d $的最大功率上，可以在给定的订单$ n^{2-2H} $中出现在大$ n $扩展中。我们猜想在大型型号中$η（h）= h $。如果是无可及的Hermitian矩阵，则具有四分之一的四面体互动，我们可以证明$η（h）\ leq 2h $;对于该模型的复杂两部分版本证明了更尖锐的$η（h）= H $，而无需施加无可笑的条件。我们还证明，具有六号车轮相互作用的Hermitian模型的$η（H）= H $，同样无需施加无可笑的条件。
We investigate the existence and properties of a double asymptotic expansion in $1/N^{2}$ and $1/\sqrt{D}$ in $\mathrm{U}(N)\times\mathrm{O}(D)$ invariant Hermitian multi-matrix models, where the $N\times N$ matrices transform in the vector representation of $\mathrm{O}(D)$. The crucial point is to prove the existence of an upper bound $η(h)$ on the maximum power $D^{1+η(h)}$ of $D$ that can appear for the contribution at a given order $N^{2-2h}$ in the large $N$ expansion. We conjecture that $η(h)=h$ in a large class of models. In the case of traceless Hermitian matrices with the quartic tetrahedral interaction, we are able to prove that $η(h)\leq 2h$; the sharper bound $η(h)=h$ is proven for a complex bipartite version of the model, with no need to impose a tracelessness condition. We also prove that $η(h)=h$ for the Hermitian model with the sextic wheel interaction, again with no need to impose a tracelessness condition.
