Special conformal transformations are a specific type of transformation that can be applied in the context of conformal field theories (CFTs) and conformal geometry. In a conformal transformation, angles are preserved, but distances may change. Special conformal transformations are a special subset of these transformations that involve a specific modification of the space-time coordinates.
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The three special conformal transformations complete translations, rotations, and dilations to the ten-dimensional de Sitter isometry group in flat slicing. A propagation speed different from the metric light speed generally breaks these transformations.