Non-SUSY $p$-branes delocalized in two directions, tachyon condensation and T-duality

We here generalize our previous construction [hep-th/0409019] of non-supersymmetric $p$-branes delocalized in one transverse spatial direction to two transverse spatial directions in supergravities in arbitrary dimensions ($d$). These solutions are characterized by five parameters. We show how these solutions in $d=10$ interpolate between D($p+2$)-anti-D($p+2$) brane system, non-BPS D$(p+1)$-branes (delocalized in one direction) and BPS D$p$-branes by adjusting and scaling the parameters in suitable ways. This picture is very similar to the descent relations obtained by Sen in the open string effective description of non-BPS D$(p+1)$ brane and BPS D$p$-brane as the respective tachyonic kink and vortex solutions on the D$(p+2)$-anti-D$(p+2)$ brane system (with some differences). We compare this process with the T-duality transformation which also has the effect of increasing (or decreasing) the dimensionality of the branes by one.