Holography of Charged Dilaton Black Holes

Understand

We study charged dilaton black branes in $AdS_4$.

• Our system involves a dilaton $\phi$ coupled to a Maxwell field $F_{\mu\nu}$ with dilaton-dependent gauge coupling, ${1\over g^2} = f^2(\phi)$.
• First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques.
• The near horizon geometries in the simplest cases, where $f(\phi) = e^{\alpha\phi}$, are Lifshitz-like, with a dynamical exponent $z$ determined by $\alpha$.