People generalize the statements of AdS/CFT correspondence by adding black hole (charged black hole) in the gravity theory to provide the dual gauge theory finite temperature (finite density). I have some problems (may be very basic) understanding these concepts with charged BH intuitively.
Is it true that whenever one adds a charged BH in the bulk one introduces conserved current (matter degrees of freedom) in the boundary? For N=4 SYM what are they?
What does the chemical potential do in dual field theory side? Actually I don't really have clear intuitive picture of chemical potential unlike pressure, temperature etc.
When one adds charge to a BH the temperature of the BH depends on both mass and charge. Now what are the independent parameters one can tune to make the BH extremal? What do these changes mean in the dual field theory picture?
This post imported from StackExchange Physics at 2015-08-22 08:20 (UTC), posted by SE-user pinu