标题： $\mathcal{N}=2$有动态玻色子和费米子的SYK模型 显示英文标题

标题： $\mathcal{N}=2$ SYK models with dynamical bosons and fermions

摘要： 我们研究了一类具有$\mathcal{N}=2$超对称性的SYK模型，该模型由位于手征费米多重态中的$N$费米子以及位于手征多重态中的$\alpha N$一阶玻色子描述。 相互作用由两个整数$(p,q)$表征。 我们关注这些模型的大$N$和低能极限。 尽管存在动力学玻色子，我们发现其共形行为类似于标准的SYK模型。 我们使用$\mathcal{I}$极值化一个Witten指标来研究超对称解。 特别是，我们找到了熵的一个精确表达式，该表达式与Schwinger-Dyson方程的数值解相匹配。 我们进一步在大$p$和大$p,q$极限下求解该模型。 数值上，我们验证了我们的解析结果，并得到了近零温度极限下的 Schwarzian 耦合估计值。 我们还研究了算符的低能谱，以确定 Schwarzian 模式主导红外动力学的参数范围。 最后，我们研究了时间反向有序关联函数，以表明该模型是最大混沌的。 显示英文摘要

摘要： We study a class of SYK models with $\mathcal{N}=2$ supersymmetry, described by $N$ fermions in chiral Fermi multiplets, as well as $\alpha N$ first-order bosons in chiral multiplets. The interactions are characterised by two integers $(p,q)$. We focus on the large $N$ and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behaviour akin to the standard SYK model. We use $\mathcal{I}$-extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large $p$ and large $p,q$ limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic.