2024/08/15 by Ahsan Z. Khan, Khan, Ahsan Z., Gregory W. Moore +1 · 1 citation
Engineering · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Optical Polarization and Ellipsometry #Optical and Acousto-Optic Technologies #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2408.08372
openalex publication_date 2024/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Algebra of the Infrared \citeGaiotto:2015aoa is a framework to construct local observables, interfaces, and categories of supersymmetric boundary conditions of massive N=(2,2) theories in two dimensions by using information only about the BPS sector. The resulting framework is known as the ``web-based formalism.'' In this paper we initiate the generalization of the web-based formalism to include a much wider class of N=(2,2) quantum field theories than was discussed in \citeGaiotto:2015aoa: theories with non-trivial twisted masses. The essential new ingredient is the presence of BPS particles within a fixed vacuum sector. In this paper we work out the web-based formalism for the simplest class of theories that allow for such BPS particles: theories with a single vacuum and a single twisted mass. We show that even in this simple setting there are interesting new phenomenon including the emergence of Fock spaces of closed solitons and a natural appearance of Koszul dual algebras. Mathematically, studying theories with twisted masses includes studying the Fukaya-Seidel category of A-type boundary conditions for Landau-Ginzburg models defined by a closed holomorphic one-form. This paper sketches a web-based construction for the category of A-type boundary conditions for one-forms with a single Morse zero and a single non-trivial period. We demonstrate our formalism explicitly in a particularly instructive example.