Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 33. Chapters: Scale invariance, Vertex operator algebra, Critical point, AdS/CFT correspondence, N = 2 superconformal algebra, Knizhnik-Zamolodchikov equations, Virasoro algebra, Polyakov action, Critical phenomena, Affine Lie algebra, Wess-Zumino-Witten model, Infrared fixed point, Super Virasoro algebra, Conformal symmetry, Yang-Baxter equation, Liouville field theory, Operator product expansion, Algebraic holography, Conformal anomaly, UV fixed point, Lie conformal algebra, Anomalous scaling dimension, C-theorem, Witt algebra, Quantum KZ equations, Banks-Zaks fixed point, Classical scaling dimension, Kerr/CFT correspondence, Primary field, Twisted sector, Coset construction, Special conformal transformation, Fusion rules, Logarithmic conformal field theory, Critical variable, Boundary conformal field theory, Minimal models, Coset conformal field theory, Sugawara theory, Rational conformal field theory, Irrational conformal field theory, Conformal family, Singleton field. Excerpt: In physics and mathematics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry. In mathematics, one can consider the scaling properties of a function or curve under rescalings of the variable . That is, one is interested in the shape of for some scale factor, which can be taken to be a length or size rescaling. The requirement for to be invariant under all rescalings is usually taken to be for some choice of exponent, and for all dilations . Examples of scale-invariant functions are the monomials, for which one has, in that clearly An example of a scale-invariant curve is the logarithmic spiral, ...