States and IR divergences in factorization algebras

Abstract

In field theory, one can consider a variety of states. Within the framework of factorization algebras, one typically works with the natural augmentation state $⟨-{⟩}_{\mathrm{aug}}$. In physics, however, other states arise naturally, such as the compactification state $⟨-{⟩}_{\mathrm{cptf}}$ or the Schwartz state $⟨-{⟩}_{\mathrm{Sch}}$, defined by imposing Schwartz boundary conditions. At first sight, the relation among these three states is not obvious. This paper gives a definition of the compactification state in factorization algebras and provides a method for handling infrared divergences in the massless theory. We then prove that the three states are equivalent in both the massive and massless cases.

28 pages, v2: corrections and a reference added