A construction of vertex algebra bundles on logarithmic smooth curves

TL;DR

This paper constructs vertex algebra bundles and conformal blocks over logarithmic smooth curves, extending previous work to more general curve types and analyzing their properties.

Contribution

It introduces a new construction of vertex algebra bundles on logarithmic curves and explores their conformal blocks, generalizing earlier results to a broader class of curves.

Findings

Established a weaker propagation of vacua

Computed conformal blocks on a nodal curve

Extended vertex algebra bundle theory to logarithmic curves

Abstract

We present a construction of vertex algebra bundles and spaces of conformal blocks over families of logarithmic smooth curves. This work generalizes some earlier results by Frenkel and Ben-Zvi on vertex algebra bundles over complex smooth algebraic curves. We establish a weaker version of the propagation of vacua, and compute the space of conformal blocks over a typical example of a nodal curve.