= Primary field
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= Primary operator
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= Virasoro primary operator
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A primary field in a two-dimensional <conformal field theory> transforms homogeneously under local conformal coordinate changes, with <conformal weights> $(h,\widetilde h)$. Its <scaling dimension> is $h+\widetilde h$ and its two-dimensional <spin> is $h-\widetilde h$.
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>.
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