nLab boundary field theory




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In FQFT-language, as a (pre-)quantum field theory in dimension nn is given by a functor on an (infinity,n)-category of cobordisms, so a field theory with boundaries/branes is given by such a functor on an (,n)(\infty,n)-category of cobordisms with marked boundaries. The assignments to the boundary data itself defines a kind of field theory of one dimension lower, which is the corresponding boundary field theory.

If the field theory is thought of as a sigma-model that describes the quantum mechanics of a particle or string or membrane, etc., then the boundary condition is also called a brane for that sigma-model.


See at


singularityfield theory with singularities
boundary condition/braneboundary field theory
domain wall/bi-braneQFT with defects


For more see the references at defect field theory.

Comments in the context of multisymplectic geometry are in

Axiomatization and examples of boundary field theories in local prequantum field theory is in

Discussion of the BV-phase space and Poisson \infty -algebras of BF theory and Einstein gravity on corners:

Last revised on November 28, 2023 at 10:21:37. See the history of this page for a list of all contributions to it.