# Field Theoretical Approach to the Phases of QCD

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The study of the phases of Quantum Chromodynamics (QCD), at finite temperature (T) and baryon chemical potential (mu_B), is one of the biggest challenges in theoretical physics and represents a significant step towards understanding the collective behavior of the strong force. The non-perturbative region of QCD, where atomic matter dissolves into a Quark-Gluon-Plasma state, can only be studied from first principles by numerical lattice simulations. These studies have established that the transition is a smooth crossover. It is expected that, as mu_B increases, the crossover sharpens into a critical-end-point (CEP) where a first order phase transition begins. However, due to the fermion sign problem, calculations on the lattice cannot be performed at real

This dissertation is devoted to exploring the high mu_B-region of QCD. First, I will analyze the lower order baryonic susceptibilities simulated on the lattice at imaginary-mu_B to calculate the higher order ones at mu_B. Those susceptibilities allow one to have access to a finite mu_B, by Taylor expanding the QCD thermodynamical potential around mu_B, and to make a direct connection with the distribution of conserved charges measured in HICs. The second part of this thesis uses a model based on the gauge/string duality to engineer holographic black holes that mimic the equation of state of QCD obtained on the lattice at mu_B and predicts its behavior at finite mu_B. Our black hole model provides a realistic prediction of the existence of a CEP in the phase diagram of QCD, located at mu_B^{CEP}=724 MeV and T_{CEP}=89 MeV. It reproduces the baryon susceptibilities calculated on the lattice at mu_B=0 and predicts them at arbitrary mu_B. Finally, the analysis made with the holographic model leads to predict the collision energy needed to hit the CEP in HICs, which is within the range of the next generation of colliders.