The pseudogap phase in cuprate superconductors is one of the most intriguing challenges in the theory of high temperature superconductivity. I elaborate on the hypothesis that pseudogap phenomena are mostly due to strong magnetic fluctuations. Using the two-dimensional Hubbard model to describe the electrons in the copper-oxygen planes of the cuprates, a gauge theory of fluctuating magnetic order is formulated and analyzed [1,2]. The theory is based on a fractionalization of electrons in fermionic chargons with a pseudospin degree of freedom and bosonic spinons. The chargons undergo Neel or incommensurate antiferromagnetic order below a density dependent transition temperature T*. Fluctuations of the spin orientation are described by a non-linear sigma model obtained from a gradient expansion of the spinon action. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order exhibits many features characterizing the pseudogap regime in high-Tc cuprates: a strong reduction of charge carrier density, a spin gap, and Fermi arcs. A substantial fraction of the pseudogap regime in the Hubbard model exhibits electronic nematicity and strong charge fluctuations.

[1] P.M. Bonetti and W. Metzner, Phys. Rev. B 106, 205152 (2022).
[2] P. Forni et al., Phys. Rev. B 113, 045144 (2026).