W-algebras and chiral differential operators at the critical Level

Details W-algebras and chiral differential operators at the critical Level W-algebras and chiral differential operators at the critical Level

2012-03-21

arxiv.org/abs/1203.4784v1

Mathematics

Representation Theory

Scientific paper

Let $\mathcal{A}_{crit}$ be the chiral algebra corresponding to the affine Kac-Moody algebra at the critical level $\hat{\mathfrak{g}}_{crit}$. Let $\mathfrak{Z}_{crit}$ be the center of $\mathcal{A}_{crit}$. The commutative chiral algebra $\mathfrak{Z}_{crit}$ admits a canonical deformation into a non-commutative chiral algebra $\mathcl{W}_{h}$. In this paper we will express the resulting first order deformation via the chiral algebra $\mathcal{D}_{crit}$ of chiral differential operators of $G((t))$ at the critical level.

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