TL;DR
This paper explores the relationship between the Virasoro algebra, chiral energy-momentum tensors, and current algebras, revealing how gauge invariance and algebra extensions relate at different levels.
Contribution
It demonstrates the equivalence of the $c=1$ Virasoro algebra with a gauge invariant subtheory of the $SU(2)$ current algebra and extends this to $W$-algebra structures at higher levels.
Findings
The $c=1$ Virasoro algebra matches a gauge invariant subtheory of the $SU(2)$ current algebra.
Higher level extensions lead to $W$-algebra structures.
The scheme links Virasoro algebra extensions to gauge invariance in quantum field theory.
Abstract
It is shown that the local quantum field theory of the chiral energy- momentum tensor with central charge coincides with the gauge invariant subtheory of the chiral current algebra at level 1, where the gauge group is the global symmetry. At higher level, the same scheme gives rise to -algebra extensions of the Virasoro algebra.
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