VYSOKÝ, J. and B. JURČO. Extended generalized geometry and a DBI-type effective action for branes ending on branes. Journal of High Energy Physics. 2014, 2014(2014:170), ISSN 1029-8479. DOI 10.1007/JHEP08(2014)170. Available from: http://link.springer.com/article/10.1007/JHEP08%282014%29170
Starting from the usual bosonic membrane action, we develop the geometry suitable for the description of p-brane backgrounds. Using the tools of generalized geometry we derive the generalization of string open-closed relations. Nambu-Poisson structures are used to generalize the concept of semiclassical noncommutativity of D-branes governed by Poisson tensor. We naturally describe the correspondence of recently proposed commutative and noncommutative versions of an effective action for p-branes ending on a p′-brane. We calculate the power series expansion of the action in background independent gauge. Leading terms in the double scaling limit are given by a generalization of a (semi-classical) matrix model.