In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, a rational conformal field theory is a special type of
two-dimensional conformal field theory
A two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations.
In contrast to other types of conformal field theories, two-dimensional conformal fie ...
with a finite number of conformal
primaries
Primary elections, or direct primary are a voting process by which voters can indicate their preference for their party's candidate, or a candidate in general, in an upcoming general election, local election, or by-election. Depending on the c ...
. In these theories, all dimensions (and the central charge) are
rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ration ...
s that can be computed from the consistency conditions of conformal field theory. The most famous examples are the so-called
minimal models.
More generally, ''rational conformal field theory'' can refer to any CFT with a finite number of primary operators with respect to the action of its chiral algebra. Chiral algebras can be much larger than the Virasoro algebra. Well-known examples include (the enveloping algebra of)
affine Lie algebra In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. Given an affine Lie algebra, one can also form the associated affine Kac-Moody a ...
s, relevant to the
Wess–Zumino–Witten model
In theoretical physics and mathematics, a Wess–Zumino–Witten (WZW) model, also called a Wess–Zumino–Novikov–Witten model, is a type of two-dimensional conformal field theory named after Julius Wess, Bruno Zumino, Sergei Novikov and Edwa ...
, and
W-algebras.
Conformal field theory
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