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In physics, Liouville field theory (or simply Liouville theory) is a two-dimensional conformal field theory whose classical equation of motion is a generalization of Liouville's equation. Liouville theory is defined for all complex values of the central charge c {\displaystyle c} of its Virasoro symmetry algebra , but it is unitary only if
While a CFT might conceivably exist only on a given Riemann surface, its existence on any surface other than the sphere implies its existence on all surfaces. [1] [2] Given a CFT, it is indeed possible to glue two Riemann surfaces where it exists, and obtain the CFT on the glued surface. [1] [3] On the other hand, some CFTs exist only on the ...
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions , there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified.
In a free bosonic CFT, the Virasoro algebra's central charge can take any complex value. However, the value c = 1 {\displaystyle c=1} is sometimes implicitly assumed. For c = 1 {\displaystyle c=1} , there exist compactified free bosonic CFTs with arbitrary values of the compactification radius.
where R is the radius of a n-dimensional sphere at time t. The radiation is represented by a (n+1)-dimensional CFT. The entropy of that CFT is then given by the formula = (), where E c is the Casimir effect, and E the total energy. The above reduced formula gives the maximal entropy
The three-state Potts CFT, also known as the parafermion CFT, is a conformal field theory in two dimensions. It is a minimal model with central charge c = 4 / 5 {\displaystyle c=4/5} . It is considered to be the simplest minimal model with a non-diagonal partition function in Virasoro characters , as well as the simplest non-trivial CFT with ...
In theoretical physics, a rational conformal field theory [1] is a special type of two-dimensional conformal field theory with a finite number of conformal primaries.In these theories, all dimensions (and the central charge) are rational numbers that can be computed from the consistency conditions of conformal field theory.
In > dimensions, superconformal primaries are annihilated by and by the fermionic generators (one for each supersymmetry generator). Generally, each superconformal primary representations will include several primaries of the conformal algebra, which arise by acting with the supercharges Q {\displaystyle Q} on the superconformal primary.