2025/01/14 by Vicedo, Benoit · 1 citation
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2501.08412
We give a systematic construction of the symmetries, or observables in the vacuum sector, of a full conformal field theory on an arbitrary real two-dimensional conformal manifold Σ. Specifically, we construct a prefactorisation algebra on Σ which locally encodes the full (non-chiral) version \mathbbF^\mathfraka,α = \mathbbV^\mathfraka,α ⊗ \mathbbV^\mathfraka,α of a universal enveloping vertex algebra \mathbbV\mathfrak a,α, where \mathfrak a is a finite-dimensional vector space labelling the set of fields and α is a 2-cocycle controlling the central extension of their Lie brackets. Our construction provides a unified treatment of the three canonical examples of (full) universal enveloping vertex algebras - Kac-Moody, Virasoro and βγ system - using the notion of unital local Lie algebra. By using the coordinate-invariant nature of prefactorisation algebras we derive an analogue of Huang's change of variable formula for full vertex algebras. We give a careful treatment of (both Euclidean and Lorentzian) reality conditions in this formalism which allows us, in the Kac-Moody and Virasoro cases, to construct a Hermitian sesquilinear form on these full vertex algebras by using the factorisation product to the global observables on S2. We also give an explicit derivation of Borcherds type identities and a construction of the operator formalism for \mathbbF\mathfrak a,α.