Plasma-Plasma Third Order Phase Transition from Type IIB Supergravity

We show that the planar, charged black hole in asymptotically anti–de Sitter spacetime, dual to the strongly coupled quark-gluon plasma thermal state of large <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi></a:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>SU</c:mi></c:mrow><c:mo stretchy="false">(</c:mo><c:mi>N</c:mi><c:mo stretchy="false">)</c:mo></c:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi mathvariant="script">N</g:mi><g:mo>=</g:mo><g:mn>4</g:mn></g:math> super Yang-Mills at finite chemical potential undergoes a third-order phase transition in the grand canonical ensemble to a hairy black hole of type IIB supergravity. The hairy phase is another strongly coupled fluid with a conformal equation of state and can be interpreted as another kind of quark-gluon plasma. This new quark-gluon plasma has less entropy and, therefore, seems to characterize some form of smooth hadronization. The locus of the transition in terms of the critical values of the “baryon” chemical potential <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>μ</j:mi><j:mi>c</j:mi></j:msub></j:math> and the temperature <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>T</l:mi><l:mi>c</l:mi></l:msub></l:math> is <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>μ</n:mi><n:mi>c</n:mi></n:msub><n:mo>=</n:mo><n:mn>2</n:mn><n:mi>π</n:mi><n:msub><n:mi>T</n:mi><n:mi>c</n:mi></n:msub></n:math>.