This survey article is an invited contribution to the Encyclopedia of Mathematical Physics,
2nd edition. We provide an accessible overview on relevant applications of higher and …

We discuss the properties of quarter-BPS local operators in four-dimensional N= 1
supersymmetric Yang-Mills theory using the formalism of holomorphic twists. We study loop …

The holomorphic twist provides a powerful framework to study minimally protected sectors in
supersymmetric quantum field theories. We investigate the algebraic structure underlying …

We develop an algebraic structure modeling local operators in a three-dimensional quantum
field theory which is partially holomorphic and partially topological. The geometric space …

We introduce a higher dimensional generalization of the affine Kac-Moody algebra using the
language of factorization algebras. In particular, on any complex manifold there is a …

We show that four-dimensional superconformal algebras admit an infinite-dimensional
derived enhancement after performing a holomorphic twist. The type of higher symmetry …

Abstract We study the Kaluza–Klein reduction of various 6 d holomorphic theories. The KK
reduction is analyzed in the BV formalism, resulting in theories that come from the …

We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions.
Working in the BV formalism, we rederive classical results characterizing the holomorphic …

Let $ X $ be a smooth affine variety over a field $\mathbf k $ of characteristic $0 $ and $ T (X)
$ be the Lie algebra of regular vector fields on $ X $. We compute the Lie algebra …

2-Chern-Simons theory, or more commonly known as 4d BF-BB theory with gauged shift
symmetry, is a natural generalization of Chern-Simons theory to 4-dimensional manifolds. It …