RESUMEN

Precisely two coadjoint orbit spaces of the group of string reparametrizations carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex manifolds. These are M₁ = Diff(S¹)/ Rot (S¹) and M₂ = Diff(S¹)/ Möb (S¹). M₂ can be naturally considered as (embedded in) the classical universal Teichmüller space T(Δ), simply by noting that at diffeomorphism of S¹ is a quasi-symmetric homeomorphism. T(Δ) is itself a holomorphically homogeneous complex Banach manifold. We prove that the inclusion of M₂ in T(Δ) is complex analytic. Every Teichmüller space of finite or infinite dimension is contained canonically and holomorphically in T(Δ). Our result thus appears to connect the loop space approach to bosonic string theory with the sum-over moduli (Polyakov path integral) approach.