Spiral spin liquids are a class of spin liquids that feature a ring degeneracy of its ground states. Over the years, a concrete physical picture of its spin liquid nature has not been established, considering that its zero-temperature ground states do not admit any local degeneracy. In this work we illustrate the low-energy structure of 2D spiral spin liquids, and reveal its connection to fracton and smectic physics. We find that the local momentum vector can form new types of momentum vortices in the system, which have very different properties from the commonly known spin vortices [1]. Their proliferation leads the system into the spin liquid phase at low temperature. Furthermore, the effective theory shows that these objects are equivalent to quadrupoles of fractons in rank-2 U(1) theory and also topological defects in smectic matter. Our work sheds light on the nature of classical spiral spin liquids, and has direct application to the material FeCl3 [2].

[1] H. Yan and J. Reuther, Low energy structure of spiral spin liquids, Phys. Rev. Research 4, 023175 (2022)
[2] Gao et al., Spiral spin-liquid on a honeycomb lattice, arXiv:2112.11327