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In AdS/CFT a charged Black hole is probably someway equivalent to introducing a chemical potential (Chemical potential) at the boundary theory. Is there a quick way to see how it is or how does this correspondence work?

I am sure it's well argued, but I haven't found a satisfactory explanation in any paper. Specially I will like to understand by connecting it with the thermodynamic case. In addition, it will be very helpful, if you can suggest me any introductory references or something with a nice explanation. Thanks!

Qmechanic
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user1349
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1 Answers1

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One can get an intuitive picture of the relation by realizing the following: in statistical physics, conserved quantities are implemented by Lagrange multipliers, see for example these lecture notes (pdf). Chemical potential is defined as the Lagrange multiplier corresponding to the conservation of charge. Now the assumption that a charged black hole might somehow be related to chemical potential is not too far-fetched. The chemical potential is identified with the $U(1)$ gauge field generated by the charge, directly affecting the boundary theory.

Additional information can be found here (pdf), in chapter 1.1.6.

Furthermore, chemical potential also can be used to describe the presence of a conserved number of particles, like it is done with baryons in holographic QCD. In this context, one speaks of a baryon chemical potential.

Frederic Brünner
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