# Master defense by Bjarke Kofoed Reimann

Decoupling Limit and Supersymmetry of $D3$-Branes in Varying Kalb-Ramond Field Backgrounds

"This thesis deals with the Dirac-Born-Infeld action describing a $D3$-brane in the background of different Kalb-Ramond fields. In the first part the decoupling limit $l_s \rightarrow 0$ of the DBI-action is taken and shown to be equivalent to $\mathcal{N}=4$ Super Yang-Mills for constant Kalb-Ramond field. For varying Kalb-Ramond field this is hypothesised to be equivalent to $\mathcal{N}=4$ SYM with varying theta-angle and Yang-Mills coupling. An action for this is derived by dimensional reduction of Abelian six-dimensional (2,0) theory on an elliptic fibration. The two actions are then compared and shown to be inequivalent.

In the second part the number of supersymmetries preserved by a $D3$-brane in different Kalb-Ramond field backgrounds is calculated. It is shown to be 1/2 BPS for zero and constant field configurations. The point charge is shown to be 1/4 BPS due to inducing a deformation of the worldsheet. Lastly a plane-wave solution to the DBI equations of motion is constructed and shown to be 1/2 BPS, lending itself to a possible future extension of the Born-Infeld gravity correspondence to a modified AdS spacetime."