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.
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A primary field in a two-dimensional conformal field theory transforms homogeneously under local conformal coordinate changes, with conformal weights . Its scaling dimension is and its two-dimensional spin is .
In the holomorphic sector, its defining operator product expansion with the stress-energy tensor is . 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.