I am trying to study what happens when we take string corrections to the gauge theory confinement-deconfinement phase transition a la Herzog.
The method to be adopted is:
First: find the contribution of the D7-brane to the total free energy (coming from Born-Infeld action). This contribution makes sense only if N_c is finite.
Second: If N_c is finite, then the D7-brane contributes a tadpole to the dilaton and axion (the latter via the Bianchii identity for F^{(1)} _{RR}). Similarly, the metric also picks up some back reaction.
Therefore, there are corrections to the bulk supergravity action as well, at O (N_f/N_c).
Thus, add all of these contributions, for a truncated geometry, a la Herzog (or Pando-Zayas) for each of thermal AdS, and AdS-Black hole backgrounds.
Then estimate the correction to the phase transition temperature - in particular what does it depend on ?
In this, we must keep T and quark mass m_q fixed.
