Chiral differential operators on abelian varieties (Q2875945)

This paper consists of two parts. In the first part, the authors show how to go from chiral differential operators on an abelian variety \(X\) (over \(\mathbb C\)) to chiral differential operators on its dual variety \(\check X\). More precisely, they construct for each non-degenerate \(\mu \in H^1(X, \Omega^1(X))\) an equivalence of groupoids \(F_{\mu}:\mathcal{CDO}(X) \rightarrow \mathcal{CDO}(\check X)\), where \(\mathcal{CDO}(X)\) is the groupoid of chiral differential operator on \(X\), see [\textit{V. Gorbounov} et al., Invent. Math. 155, No. 3, 605--680 (2004; Zbl 1056.17022)]. The second part is a description of the quantum \(\sigma\)-model on the torus in terms of vertex algebra structures in the sense of \textit{A. Kapustin} and \textit{D. Orlov} [Commun. Math. Phys. 233, No. 1, 79--136 (2003; Zbl 1051.17017)].NEWLINENEWLINEFor the entire collection see [Zbl 1285.00037].