Four-Dimensional Avatars of Two-Dimensional RCFT

TL;DR

This paper explores a four-dimensional analog of 2D WZW theory, revealing its finiteness, infinite-dimensional symmetry, and defining key structures like correlation functions, vertex operators, and conformal blocks, with an analog of the Verlinde formula.

Contribution

It introduces a novel 4D theory extending 2D WZW models, establishing its symmetry, correlation functions, and conformal blocks, and proposing a new quantization approach.

Findings

The 4D theory exhibits surprising finiteness properties.

It possesses an infinite-dimensional current algebra symmetry.

Correlation functions are determined by this symmetry.

Abstract

We investigate a 4D analog of 2D WZW theory. The theory turns out to have surprising finiteness properties and an infinite-dimensional current algebra symmetry. Some correlation functions are determined by this symmetry. One way to define the theory systematically proceeds by the quantization of moduli spaces of holomorphic vector bundles over algebraic surfaces. We outline how one can define vertex operators in the theory. Finally, we define four-dimensional ``conformal blocks'' and present an analog of the Verlinde formula.