A Fermi surface coupled to a scalar field can be described in a $1/N$ expansion by choosing the fermion-scalar Yukawa coupling to be random in the $N$-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and verify that the proposed $1/{\omega }^{2/3}$ contribution to the optical conductivity at frequency $\omega$ has vanishing coefficient for a convex Fermi surface. We also describe the influence of impurity scattering of the fermions, and find that while the self-energy resembles a marginal Fermi liquid, the resistivity and optical conductivity behave like a Fermi liquid.

中文翻译：

---

临界费米面的大 N 理论。二、电导率

耦合到标量场的费米面可以描述为$1/ñ$通过选择费米子标量 Yukawa 耦合在$ñ$维风味空间，但在平移下不变。我们在临界标量的两个空间维度上计算了这种理论的电导率。我们找到了 Drude 的贡献，并验证了提议的$1/{\omega }^{2/3}$对频率光导率的贡献$\omega$具有凸费米面的消失系数。我们还描述了费米子的杂质散射的影响，发现虽然自能类似于边缘费米液体，但电阻率和光导率表现得像费米液体。