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In FQFT-language, as a (pre-)quantum field theory in dimension $n$ 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 $(\infty,n)$-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
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For more see the references at defect field theory.
Comments in the context of multisymplectic geometry are in
General Boundary Field Theory_, (pdf)
Axiomatization and examples of boundary field theories in local prequantum field theory is in
Domenico Fiorenza, Alessandro Valentino, Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors (arXiv:1409.5723)
Last revised on September 23, 2014 at 20:42:01. See the history of this page for a list of all contributions to it.