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Conformal may refer to: Conformal (software), in ASIC Software; Conformal coating in electronics; Conformal cooling channel, in injection or blow moulding; Conformal field theory in physics, such as: Boundary conformal field theory; Coset conformal field theory; Logarithmic conformal field theory; Rational conformal field theory
In theoretical physics, the anti-de Sitter/conformal field theory correspondence (frequently abbreviated as AdS/CFT) is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) that are used in theories of quantum gravity , formulated in terms of string theory or M-theory .
The term conformal field theory has sometimes been used with the meaning of two-dimensional conformal field theory, as in the title of a 1997 textbook. [5] Higher-dimensional conformal field theories have become more popular with the AdS/CFT correspondence in the late 1990s, and the development of numerical conformal bootstrap techniques in the ...
The conformal field theory is often viewed as living on the boundary of the higher dimensional space whose gravitational theory it defines. The result of such a duality is a dictionary between the two equivalent descriptions.
Alternatively any conformal linear transformation can be represented as a versor (geometric product of vectors); [1] every versor and its negative represent the same transformation, so the versor group (also called the Lipschitz group) is a double cover of the conformal orthogonal group.
A conformal manifold is a Riemannian manifold (or pseudo-Riemannian manifold) equipped with an equivalence class of metric tensors, in which two metrics g and h are equivalent if and only if =, where λ is a real-valued smooth function defined on the manifold and is called the conformal factor.
We say that ~ is (pointwise) conformal to . Evidently, conformality of metrics is an equivalence relation. Evidently, conformality of metrics is an equivalence relation. Here are some formulas for conformal changes in tensors associated with the metric.
The analog of the S-matrix relations in AdS space is the boundary conformal theory. [1] The most lasting legacy of the theory is string theory. Other notable achievements are the Froissart bound, and the prediction of the pomeron.