Types of quantum field thories
abstract duality: opposite category,
If this is the case, it makes sense to ask if itself is the curvature -form of a circle -bundle with connection , where is the dimension of .
In the special case of ordinary electromagnetism with and we have that electrically charged 0-dimensional particles couple to and magnetically charged -dimensional particles couple to .
In analogy to this case one calls generally the -dimensional objects coupling to the magnetic duals of the -dimensional objects coupling to .
In heterotic string theory one considers 1-dimensional objects in -dimensional spaces electrically charged (under the Kalb-Ramond field). Their magnetic duals are 5-dimensional objects (fivebranes), studied in dual heterotic string theory.
An exposition of the relation to geometric Langlands duality is given in