We consider the finite temperature phase diagram of holographic QCD in the Veneziano limit ($N_c\to \infty$, $N_f\to \infty$ with $x_f=N_f/N_c$ fixed) and calculate one string loop corrections to the free energy in certain approximations. Such corrections, especially due to the pion modes, are unsuppressed in the Veneziano limit. We find that under some extra assumptions the first order transition following from classical gravity solutions can become second order. If stringy asymptotics are of a special form and there are residual interactions, it may even become of third order. Operationally these computations imply modeling the low temperature chiral symmetry breaking phase with a hadron gas containing $N_f^2$ massless Goldstone bosons and an exponential spectrum of massive hadrons. A third order transition is possible only if repulsive hadron interactions via the excluded volume effect are included.

• Received 30 January 2015

DOI:https://doi.org/10.1103/PhysRevD.91.055017