I encountered compactifying a 5D black string along an extra dimension in Natsuume's AdS/CFT text. Upon compactification, the thermodynamics of a 4D black hole may be identified with the 5D black string with the exception of an additional pressure term. The pressure appears due to the matter species which arise from the compactification of the additional dimension.

I have the following questions;

  1. What types of gauge fields arise from compactification?
  2. Do the species depend on how many dimensions are compactified?

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