Identify the actual symmetry group underlying bosonic string quantisation

Determine the symmetry group that should underlie the quantum formulation of the bosonic string worldsheet—beyond assuming the central extension of the Witt algebra (the Virasoro algebra)—so that the BRST cohomological construction of physical states and the treatment of Lorentz, diffeomorphism, and Weyl symmetries are justified by the correct group structure rather than by a presumed extension chosen for technical convenience.

Background

In standard string quantisation, the classical Witt algebra of diffeomorphisms on the circle is extended by a 2‑cocycle to the Virasoro algebra to accommodate quantum effects and central charge. The BRST framework then uses ghost fields to implement gauge fixing and select physical states via cohomology, with anomaly cancellation achieved in the critical dimension (D=26 for the bosonic string).

The paper argues that while this construction is mathematically consistent, it may reflect a choice driven by technical needs rather than the actual symmetry group nature intends. The author raises the possibility that the true group structure compatible with quantum mechanics and all relevant symmetries (Lorentz, diffeomorphism, Weyl) might differ from the Virasoro extension, and that identifying it could clarify the origin of anomalies and dualities from a higher-categorical or synthetic-geometric perspective.