Vertex operator algebra theory

Vertex operator algebra (VOA) theory is a branch of mathematics that studies algebraic structures modeling symmetries and interactions in two-dimensional conformal field theories, which originate in physics. It formalizes how operators—mathematical entities representing physical quantities—interact and combine, encoding deep symmetries like those found in string theory and quantum physics. VOAs provide a rigorous language to explore these complex interactions, connecting areas like algebra, geometry, and mathematical physics. In essence, VOA theory offers a powerful framework to understand how fundamental symmetries manifest and organize in advanced mathematical and physical systems.