Short distance expansion from the dual representation of infinite dimensional Lie algebras (Q1889927)

Virasoro algebra and its representations are a central concept in string and low-dimensional gravitational theories. Among these representations, the coadjoint representation presents special interest, since it relates the orbits with unitary representations, and provides an important connection with the geometric actions. In this article a realisation-free method to obtain short distance expansions from the dual representation of infinite Lie algebras is developed, i.e., using only the properties of the adjoint and coadjoint representation of infinite dimensional Lie algebras. To this extent, elements in these representations are regarded as phase-space conjugate variables, which induce a Poisson-bracket structure. The method is implemented with some fundamental algebras, such as affine Lie algebras, the Virasoro algebra and the geometrically realized \(\mathcal{GR}\) Virasoro algebra and a particular supersymmetric extension of the latter for an arbitrary number of supersymmetries whose coadjoint representation is realized by means of fermionic and bosonic derivative operators.