A two-dimensional conformal field theory is invariant under local holomorphic and antiholomorphic conformal transformations.
A primary operator of weights transforms covariantly under local conformal maps and has a universal operator-product expansion with the stress-energy tensor.
The conformal weights determine the response of a primary operator to holomorphic and antiholomorphic coordinate rescaling. Its scaling dimension is and its spin is .
An operator product expansion expresses the short-distance product of local operators as a sum of local operators multiplied by singular coefficient functions.
The holomorphic stress-energy tensor generates infinitesimal holomorphic conformal transformations through its operator product expansions.
Normal ordering removes self-contractions from a composite operator. For free fields it places annihilation modes to the right of creation modes.
Wick theorem expresses a product of free fields as its normal-ordered product plus all possible contractions.
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Two-dimensional Conformal Field Theory (2D CFT) is a branch of theoretical physics that studies two-dimensional quantum field theories that are invariant under conformal transformations. These transformations include translations, rotations, dilations (scaling), and special conformal transformations, which preserve angles but not necessarily lengths. ### Key Features of 2D CFT: 1. **Conformal Symmetry**: In two dimensions, the conformal group is infinite-dimensional.