Short Distance Expansion from the Dual Representation of Infinite Dimensional Lie Algebras
S. James Gates Jr, W.D. Linch III, J. Phillips, V.G.J. Rodgers
TL;DR
This paper develops a method to compute short distance expansions of operators in the coadjoint representation of infinite dimensional Lie algebras, including Virasoro and affine Lie algebras, using properties of the adjoint representation.
Contribution
It introduces a novel approach to derive short distance expansions solely based on the adjoint representation properties for various infinite dimensional Lie algebras.
Findings
Explicit short distance expansions for Virasoro algebra duals
Derived expansions for affine Lie algebra duals
Extended method to N-extended supersymmetric Virasoro algebra
Abstract
We compute the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional Lie algebra by using only properties of the adjoint representation and its dual. We explicitly compute the short distance expansion for the duals of the Virasoro algebra, affine Lie Algebras and the geometrically realized N-extended supersymmetric GR Virasoro algebra.
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