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A lot of attention has been drawn to superconductivity in UTe$_2$, withsuggestions of time-reversal symmetry breaking triplet chiral superconductingorder parameter. The chirality of the order parameter has been attributed to anaccidental near degeneracy of two superconducting components belonging to 1Dirreps $B_{2u}$ and $B_{3u}$ of the relevant $D_{2h}$ point group, and it hasbeen argued that the chiral $B_{2u}+iB_{3u}$ combination is selected byferromagnetic fluctuations. In this work we present a possible explanation ofthe near-degeneracy as a result of an accidental $C_4$ symmetry of the bandstructure, with the superconducting order parameter belonging the 2D $E_u$irrep of $D_{4h}$ that uniquely descends to the sought after $B_{2u}+iB_{3u}$combination. We show that the $C_4$ symmetry is emergent at the level of theinteractions using a renormalization group calculation and argue that thechiral combination of the order parameter is favored when spin-orbit couplingis added to the model.

Chiral Superconductivity in UTe$_2$ via Emergent $C_4$ Symmetry and Spin Orbit Coupling