First-order deformations of vertex algebras
- A+
：Fei Qi (Sun Yat-sen University Zhuhai Campus)
： 2026-03-06 10:30
：Conference Room S102 at Experiment Building at Haiyun Campus
Speaker：Fei Qi (Sun Yat-sen University Zhuhai Campus)
Time：2026-3-6 10:30
Location：Conference Room S102 at Experiment Building at Haiyun Campus
Abstract:
Deformation theory of vertex algebras is an important yet difficult problem in both mathematics and physics. We approach this problem by computing the second cohomology $H^2_{1/2}(V, V)$ constructed by Yi-Zhi Huang. Joint with Vladimir Kovalchuk, we created an algorithm for classifying all the first-order deformations of freely generated vertex algebras. Using these results, we explicitly determine the first-order deformations of the universal Virasoro VOA $Vir_c$, universal affine VOA $V^l(\g)$, Heisenberg VOA $V^l(\h)$, and the universal Zamolodchikov VOA $W_3^c$. It has long been conjectured that rational vertex algebras are deformation rigid, i.e., they admit no first-order deformations. In the recent work joint with Andrew Linshaw, we proved this conjecture for simple affine VOA with positive integer levels.
