In this article, we introduce basic aspects of the algebraic notion Koszul duality for a physics audience. We then review its appearance in physical problem coupling QFTs to topological line defects, and illustrate concept with some examples drawn from twists various simple supersymmetric theories. Though much content article is well-known experts, presentation have not, our knowledge, appeared...

Present day quantum field theory (QFT) is founded on canonical quantization, which has served quite well, but also led to several issues. The free describing a particle (with no interaction term) can suddenly become nonrenormalizable the instant suitable term appears. For example, using $\varphi^4_4$, been deemed ``free" with difference from truly [1], [2], [3]. Using same model, affine quantiz...

In order to construct examples for interacting quantum field theory models, the methods of euclidean field theory have turned out to be a powerful tools since they make use of the techniques of classical statistical mechanics. Starting from an appropriate set of euclidean 3⁄4 -point functions (Schwinger distributions), a Wightman theory can be reconstructed by an application of the famous Oster...