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Luis Alvarez Consul: Lectures

January 10, 2023
TITLE: Embedding superconformal vertex algebras from Killing spinors and (0,2) mirror symmetry

ABSTRACT: I will construct embeddings of the N=2 superconformal vertex algebra under appropriate conditions inspired by the Killing spinor equations in supergravity. Firstly, when these equations are formulated on a quadratic Lie algebra, they become purely algebraic conditions that induce an embedding in the corresponding superaffine vertex algebra. Secondly, when they are formulated on a suitable class of Courant algebroids, they induce an embedding in the vertex algebra of global sections of the corresponding chiral de Rham complex. As an application, I will present an example of (0,2) mirror symmetry given by pairs of homogeneous Hopf surfaces equipped with a Bismut-flat pluriclosed metric. Joint work with Andoni De Arriba De La Hera and Mario Garcia-Fernandez (arxiv:2012.01851, to appear in IMRN, and further work in progress).

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