 Primary field

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.

The term "primary field" can refer to different concepts depending on the context in which it's used. Here are a few interpretations: 1. **Data Management**: In databases, a primary field (or primary key) is a unique identifier for each record in a table. It ensures that each entry can be uniquely identified and accessed, preventing duplicates.