Boundary Chiral Algebras and Holomorphic Twists

We study the holomorphic twist of 3d $$\mathcal{N}=2$$ gauge theories in presence boundaries, and algebraic structure bulk boundary local operators. In twist, both operators form chiral algebras (a.k.a. vertex algebras). The algebra is commutative, endowed with a shifted Poisson bracket “higher” stress tensor; while module for bulk, may not be or have tensor. explicitly construct free Landau–Ginzburg models. matter and/or Chern–Simons couplings, leaving full description to future work. briefly discuss higher A-infinity like structures.