Symmetry group of a unitary CFT

Establish that the automorphism group of a unitary Conformal Field Theory, i.e., the group of linear automorphisms of the graded space of states H preserving all Segal-axiomatic structures (including the Virasoro actions and the operator product expansion), is a compact Lie group whose dimension is at most dim H^{1,0}.

Background

For a given CFT, the group of symmetries consists of automorphisms of the bigraded space of states H that preserve the full suite of algebraic structures, including the Virasoro and anti-Virasoro actions and OPE data. The conjecture asserts strong structural constraints on this symmetry group.

The claim parallels expectations from rational CFTs and lattice models, proposing Lie-theoretic and compactness properties together with a quantitative bound linked to the dimension of the subspace H^{1,0}.