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A primary field in a two-dimensional conformal field theory transforms homogeneously under local conformal coordinate changes, with conformal weights $(h,\tilde{h})$. Its scaling dimension is $h+\tilde{h}$ and its two-dimensional spin is $h-\tilde{h}$.

In the holomorphic sector, its defining operator product expansion with the stress-energy tensor is $T(z)\mathcal{O}(w)\sim h\mathcal{O}(w)/(z-w{)}^2+\partial \mathcal{O}(w)/(z-w)$. The double pole encodes rescaling and the simple pole translation. Acting with negative Virasoro algebra modes generates Virasoro descendants. This separates each family into a primary starting point and symmetry-generated operators, greatly reducing the independent information needed to specify correlation functions.

A scalar primary operator transforms without a spin rotation and is characterized by its scaling dimension. Conformal symmetry fixes its two- and three-point functions up to constants, while a four-point function can depend on conformal cross-ratios.

A discrete renormalization group with length factor $b>1$ and positive relevant thermal multiplier ${\lambda }_t>1$ sends $t$ to ${\lambda }_{t}t$ and the correlation length to $\xi /b$. Combining this with $\xi \sim |t{|}^{-\nu }$ gives the displayed correlation-length critical exponent. The corresponding scaling dimension is $y_t=\log {\lambda }_t/\log b=1/\nu$. Relevance of discrete multipliers is determined by magnitude relative to one, unlike the sign criterion for continuous-flow eigenvalues.