The polarization of Cosmic Microwave Background (CMB) photons is rotated as they pass through (ultralight-) axion string loops. Studying this birefringence can reveal valuable information about the axion-photon coupling and the structure of the string network. We develop an approximate analytic formalism and identify a kernel function that can be used to calculate the two-point correlation function for CMB birefringence induced by an arbitrary axion string network. Using this formalism, we evaluate the birefringence signal for some simple loop distributions (including scaling and network collapse). We find that the angular correlation function has a characteristic angular scale set by θ_min, which corresponds to the angular extent of the loops at the time of recombination. This results in a peak in the birefringence power spectrum around ℓ_p ∼ 1/θ_min. An additional scale, controlled by the axion's mass, is introduced if the network collapses beforetoday.

宇宙微波背景 (CMB) 光子的偏振在它们穿过（超轻）轴子弦环时会发生旋转。研究这种双折射可以揭示有关轴子-光子耦合和弦网络结构的有价值的信息。我们开发了一种近似解析形式并确定了一个核函数，该核函数可用于计算由任意轴子弦网络引起的 CMB 双折射的两点相关函数。使用这种形式，我们评估了一些简单环路分布（包括缩放和网络崩溃）的双折射信号。我们发现角相关函数具有由 θ _{min设置的特征角尺度}，这对应于重组时环的角度范围。这导致双折射功率谱在 ℓ _p ∼ 1/θ _min附近出现峰值。如果网络在今天之前崩溃，则会引入由轴子质量控制的额外尺度。