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We show that AdS black holes dual to field theories on flat spacetime, asused in applications of the AdS/CFT correspondence to strong interaction andcondensed matter physics, have temperatures with positive lower bounds. Thereare two distinct effects involved. For low chemical potentials in the dualfield theory, the cooling black hole makes a transition to a statecorresponding to confinement in the field theory. For high chemical potentials,it becomes unstable to a non-perturbative string effect. This allows aholographic sketch of the field theory phase diagram, one which is inqualitative agreement with the phenomenological understanding of the theory at[relatively] low temperatures. It also puts an interesting upper bound on thetemperature-normalized chemical potential $\bar{\mu}$ of the field theory, ifit describes a plasma: in the normalization of Myers et al., $\bar{\mu}$ mustbe less than approximately 0.49. Thus, the extent to which a chemical potentialcan worsen violations of the KSS bound is severely restricted.

Bounding the Temperatures of Black Holes Dual to Strongly Coupled Field Theories on Flat Spacetime