On higher curvature corrections to the (abelian) DBI-action for (single) D-branes:
Oleg Andreev, Arkady Tseytlin, Partition-function representation for the open superstring effective action:: Cancellation of Möbius infinites and derivative corrections to Born-Infeld lagrangian, Nuclear Physics B Volume 311, Issue 1, 19 December 1988, Pages 205-252 (doi:10.1016/0550-3213(88)90148-4)
Constantin Bachas, P. Bain, Michael Green, Curvature terms in D-brane actions and their M-theory origin, JHEP 9905:011, 1999 (arXiv:hep-th/9903210)
Niclas Wyllard, Derivative corrections to D-brane actions with constant background fields, Nucl. Phys. B598 (2001) 247-275 (arXiv:hep-th/0008125)
Oleg Andreev, More About Partition Function of Open Bosonic String in Background Fields and String Theory Effective Action, Phys. Lett. B513:207-212, 2001 (arXiv:hep-th/0104061)
Niclas Wyllard, Derivative corrections to the D-brane Born-Infeld action: non-geodesic embeddings and the Seiberg-Witten map, JHEP 0108 (2001) 027 (arXiv:hep-th/0107185)
Mohammad Garousi, T-duality of curvature terms in D-brane actions, JHEP 1002:002, 2010 (arXiv:0911.0255)
Mohammad Garousi, S-duality of D-brane action at order , Phys. Lett. B701:465-470, 2011 (arXiv:1103.3121)
Ali Jalali, Mohammad Garousi, On D-brane action at order , Phys. Rev. D 92, 106004 (2015) (arXiv:1506.02130)
Mohammad Garousi, An off-shell D-brane action at order in flat spacetime, Phys. Rev. D 93, 066014 (2016) (arXiv:1511.01676)
Komeil Babaei Velni, Ali Jalali, Higher derivative corrections to DBI action at order, Phys. Rev. D 95, 086010 (2017) (arXiv:1612.05898)
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