Boundary Chiral Algebras and Holomorphic Twists

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

Automated summary

We study the holomorphic twist of 3d N=2 gauge theories in the presence of boundaries, and examine the algebraic structure of bulk and boundary local operators. Both bulk and boundary local operators form chiral algebras in the holomorphic twist. The bulk algebra is commutative and equipped with a shifted Poisson bracket and a higher stress tensor, while the boundary algebra is a module for the bulk, may not be commutative, and may or may not have a stress tensor. We construct bulk and boundary algebras for free theories and Landau-Ginzburg models, and boundary algebras for gauge theories with matter and/or Chern-Simons couplings, leaving a complete description of bulk algebras for future work. We also discuss the presence of higher A-infinity like structures.