We review in detail the Batalin–Vilkovisky formalism for Lagrangian field theories and its
mathematical foundations with an emphasis on higher algebraic structures and classical …

We formulate differential cohomology and Chern-Weil theory--the theory of connections on
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …

It was recently argued that quantum field theories possess one‐form and higher‐form
symmetries, labelled 'generalized global symmetries.'In this paper, we describe how those …

A bstract We develop quantization techniques for describing the nonassociative geometry
probed by closed strings in flat non-geometric R-flux backgrounds M. Starting from a suitable …

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 …

The product of local operators in a topological quantum field theory in dimension greater
than one is commutative, as is more generally the product of extended operators of …

We promote geometric prequantization to higher geometry (higher stacks), where a
prequantization is given by a higher principal connection (a higher gerbe with connection) …

A bstract We point out that the one-particle-irreducible vacuum correlation functions of a QFT
are the structure constants of an L∞-algebra, whose Jacobi identities hold whenever there …

Starting with minimal requirements from the physical experience with higher gauge theories,
ie gauge theories for a tower of differential forms of different form degrees, we discover that …

The world-volume theory of coincident M5-branes is expected to contain a nonabelian 2-
form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory …