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 List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

, 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 fi ...

with a finite number of conformal

primaries Primary elections or primaries are elections held to determine which candidates will run in an upcoming general election. In a partisan primary, a political party selects a candidate. Depending on the state and/or party, there may be an "open pri ...

. 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 (for example, The set of all ...

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 ...

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 Ed ...

, and W-algebras.

References

Conformal field theory {{quantum-stub