Massless free scalar bosons are a family of two-dimensional conformal field theories, whose symmetry is described by an abelian affine Lie algebra.
Since they are free i.e. non-interacting, free bosonic CFTs are easily solved exactly. Via the Coulomb gas formalism, they lead to exact results in interacting CFTs such as minimal models. Moreover, they play an important role in the worldsheet approach to string theory.
In a free bosonic CFT, the Virasoro algebra's central charge can take any complex value. However, the value is sometimes implicitly assumed. For , there exist compactified free bosonic CFTs with arbitrary values of the compactification radius.
