标题： 任意$q$SYK 模型的三维视图 显示英文标题

标题： Three Dimensional View of Arbitrary $q$ SYK models

摘要： 在\url{arXiv:1704.07208}中，已经证明了具有四费米子相互作用的SYK模型的谱和双局域传播子可以在$AdS_2 \times S^1/Z_2$的三维模型中实现，且额外维度具有非平凡边界条件。本文中我们证明了对于具有$q$费米子相互作用的SYK模型推广形式，类似的图景同样成立。三维实现现在被给定在一个空间上，该空间的度规与$AdS_2 \times S^1/Z_2$共形，并且除了区间中心处的 δ 函数外，还受到一个非平凡势的作用。文中展示了霍拉瓦-温特紧致化可以精确重现SYK模型的谱，且位于区间中心的两点之间的非标准传播子与双局域传播子完全一致。作为$q \rightarrow \infty$，区间中心某模式的波函数以$1/q$的方式消失，而其余模式则以$1/q^2$的方式消失，这与在SYK模型中只有单一模式对双局域传播子有贡献这一事实一致。 显示英文摘要

摘要： In \url{arXiv:1704.07208} it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional model in $AdS_2 \times S^1/Z_2$ with nontrivial boundary conditions in the additional dimension. In this paper we show that a similar picture holds for generalizations of the SYK model with $q$-fermion interactions. The 3D realization is now given on a space whose metric is conformal to $AdS_2 \times S^1/Z_2$ and is subject to a non-trivial potential in addition to a delta function at the center of the interval. It is shown that a Horava-Witten compactification reproduces the exact SYK spectrum and a non-standard propagator between points which lie at the center of the interval exactly agrees with the bilocal propagator. As $q \rightarrow \infty$, the wave function of one of the modes at the center of the interval vanish as $1/q$, while the others vanish as $1/q^2$, in a way consistent with the fact that in the SYK model only one of the modes contributes to the bilocal propagator in this limit.