nLab 4d TQFT




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Functorial quantum field theory



TQFT of dimension 4.


In analogy to how 3d TQFTs are induced from quantum groups/Hopf algebras/ and generally bialgebras (hence 3-modules, the higher space of quantum states assigned to the point which by the cobordism theorem defines the theory) one may build 4d TQFTs from higher analogs of these, namely models of 4-modules given by algebraic structures such as trialgebras and Hopf categories.



Original references:

See also

  • Scott Carter, Louis Kauffman, Masahico Saito, Diagrams, Singularities, and Their Algebraic Interpretations, in “10th Brazilian Topology Meeting, S. Carlos, July 22 26, 1996 (pdf)

Construction via factorization homology from braided tensor categories (with relation to double affine Hecke algebras) is discussed in

From fully dualizable braided tensor categories, via the cobordism hypothesis:

As descriptions of topological insulators/topological phases of matter:

Many more references should eventually go here…

Last revised on December 24, 2021 at 16:00:42. See the history of this page for a list of all contributions to it.