Holographic Hagedorn temperature: Strong coupling, flavor, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>θ</mml:mi></mml:math>-angle effects

We study the Hagedorn temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>T</a:mi><a:mi>H</a:mi></a:msub></a:math> of strongly coupled quantum field theories admitting a holographic string or M-theory description in various regimes and scenarios. In the first part of the paper we propose a “thermal scalar” effective approach to the calculation of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>T</c:mi><c:mi>H</c:mi></c:msub></c:math> in eleven-dimensional supergravity. The proposal allows us to extend the existing results for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>T</e:mi><e:mi>H</e:mi></e:msub></e:math> to the strongly coupled string regime, i.e. to a previously unexplored regime of field theory parameters where the number of colors <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>N</g:mi></g:math> is smaller than (some power of) the ’t Hooft coupling <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>λ</i:mi></i:math>. We can thus extend the existing results for the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>α</k:mi><k:mo>′</k:mo></k:msup></k:math> expansion of the Aharony-Bergman-Jafferis-Maldacena model, which have a spectacular agreement with predictions from integrability, in a different direction in parameter space. In particular, we explicate the first nonperturbative corrections. We also apply the formalism to the Witten-Yang-Mills model, finding that the result for the ratio of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>T</m:mi><m:mi>H</m:mi></m:msub></m:math> with the deconfinement temperature is in the same ballpark of the lattice one for pure Yang-Mills. Within the same model, we study the dependence of the Hagedorn temperature on the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>θ</o:mi></o:math>-angle. In the second part of the paper we analyze the effect of dynamical flavors on <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>T</q:mi><q:mi>H</q:mi></q:msub></q:math> in confining theories. By studying the few available examples of regular backgrounds dual to confining theories with flavors, we find that generally the effects of flavors is to reduce the value of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>T</s:mi><s:mi>H</s:mi></s:msub></s:math> in units of the square root of the confining string tension. The effect turns out to be milder than the analogous reduction of the critical temperature for deconfinement when the latter is known.