Types of quantum field thories
abstract duality: opposite category,
FQFT and cohomology
In string theory a given Riemann surface with punctures can usually be read in different ways as describing either closed strings or open strings. For instance the disk-diagram describes equivalently a process where a closed string disappears, or a process where an open string first appears and then disappears.
Since closed string excitations induce gravity while open string excitations induce Yang-Mills fields as effective field theories, this leads to a multitude of relations between these ordinary quantum field theories, such as the KLT relations or the AdS/CFT correspondence.