This lecture extends bosonization from the bc ghost system to the commuting βγ (superghost) system, motivated by the need for vertex operators (e.g. Ramond ground-state-like objects) that have simple exponential form in a bosonized language but no simple polynomial expression in β, γ directly. A naive analog of the bc→bosonic-current construction (β,γ ~ e^{∓Φ}) fails because β, γ have opposite relative statistics-driven signs in their OPEs compared to b, c; the fix is to dress the exponentials with an auxiliary anticommuting (η,ζ) bc-type system: β = e^{-Φ}∂ζ, γ = e^{Φ}η, where Φ is a bosonic scalar with ⟨Φ(z)Φ(0)⟩ = −log z. This reproduces every βγ OPE sign correctly, and matching the resulting stress tensor (via the T(z)βγ(0) OPE) to the known βγ stress tensor fixes Φ's background-charge (linear dilaton) term, analogous to the bc-to-bosonization dictionary. This belongs to superstring worldsheet CFT (superghost bosonization), essential for constructing Ramond-sector and picture-changed vertex operators in the RNS formalism.
This lecture extends bosonization from the bc ghost system to the commuting βγ (superghost) system, motivated by the need for vertex operators (e.g. Ramond ground-state-like objects) that have simple…