DBI equations and holographic DC conductivity

Understand

We provide a simple method for writing the Dirac-Born-Infeld (DBI) equations of a Dp-brane in an arbitrary static background whose metric depends only on the holographic radial coordinate z.

• Using this method we revisit the Karch-O'Bannon's procedure to calculate the DC conductivity in the presence of constant electric and magnetic fields for backgrounds where the boundary is four or three dimensional and satisfies homogeneity and isotropy.
• We find a frame-independent expression for the DC conductivity tensor.
• For particular backgrounds we recover previous results on holographic metals and strange metals.