${\rm
  Re}[\mathcal{S}_{2\delta}^+]$, ${\rm Im}[\mathcal{S}_{2\delta}^+]$, and $\mathcal{S}_0^z$, become the uniform magnetization operator ${\bm
  L} = {\bm J}_R + {\bm J}_L$, where ${\bm J}_{R/L}$ are the chiral spin currents (scaling dimension 1). The remaining operator, ${\rm
  Im}[\mathcal{S}^z_{\pi-2\delta}]$ becomes the staggered dimerization field $\varepsilon$ (scaling dimension 1/2).

DM-ology {#sec:dm-ology}
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Here we present the DM terms which correct the standard model, as allowed by the space group symmetry of the lattice. They are derived in Appendix \[sec:dmv\]. Since [[Cs$_2$CuCl$_4$]{}]{} is an $S=1/2$ system with a single unpaired electron in a non-degenerate orbital, we expect that spin-orbit effects to be perturbative. In this limit, the leading effect is to generate DM terms on the same bonds on which exchange interactions are present, and which are proportional to both the exchange coupling on that bond, and to the strength of spin orbit interactions. As a consequence, we need to consider DM terms only on bonds with reasonably strong exchange, that is, the intra-layer triangular lattice bonds. These come in two types: the on-chain bonds and the diagonals. We denote the DM vectors on the former bonds by ${\bm D}$ and on the latter by ${\bm D}'$, in analogy to $J$ and $J'$ exchange couplings on 