We construct a class of bottom-up holographic models with physics comparable to the one expected from QCD in the Veneziano limit of large N f and N c with fixedNc . The models capture the holographic dynamics of the dilaton (dual to the YM coupling) and a tachyon (dual to the chiral condensate), and are parametrized by the real parameter x, which can take values within the range 0 ≤ x < 11 2 . We analyze the saddle point solutions, and draw the phase diagram at zero temperature and density. The back-reaction of flavor on the glue is fully included. We find the conformal window for x ≥ x c , and the QCD-like phase with chiral symmetry breaking at x < x c , where the critical value x c lies close to four. We also find Miransky scaling as x → x c as well as Efimov-like saddle points. By calculating the holographic β-functions, we demonstrate the "walking" behavior of the coupling in the region near and below x c .

Zero temperature spectra of mesons and glueballs are analyzed in a class of holographic bottom-up models for QCD in the Veneziano limit, N c

Holographic models in the T = 0 universality class of QCD in the limit of large number N c of colors and N f massless fermion flavors, but constant ratio x f = N f /N c , are analyzed at finite temperature. The models contain a 5-dimensional metric and two scalars, a dilaton sourcing TrF 2 and a tachyon dual toqq. The phase structure on the T, x f plane is computed and various 1st order, 2nd order transitions and crossovers with their chiral symmetry properties are identified. For each x f , the temperature dependence of p/T 4 and the condensate qq is computed. In the simplest case, we find that for x f up to the critical x c ∼ 4 there is a 1st order transition on which chiral symmetry is broken and the energy density jumps. In the conformal window x c < x f < 11/2, there is only a continuous crossover between two conformal phases. When approaching x c from below, x f → x c , temperature scales approach zero as specified by Miransky scaling.

We use the holographic V-QCD models to analyse the physics of dense QCD and neutron stars. Accommodating lattice results for thermodynamics of QCD enables us to make generic predictions for the Equation of State (EoS) of the quark matter phase in the cold and dense regime. We demonstrate that the resulting pressure in V-QCD matches well with a family of neutron-star-matter EoSs that interpolate between state-of-the-art theoretical results for low and high density QCD. After implementing the astrophysical constraints, i.e., the largest known neutron star mass and the recent LIGO/Virgo results for the tidal deformability, we analyse the phase transition between the baryonic and quark matter phases. We find that the baryon density n B at the transition is at least 2.9 times the nuclear saturation density n s . The transition is of strongly first order at low and intermediate densities, i.e., for n B /n s 7.5.

The holographic model of V-QCD is used to analyze the physics of QCD in the Veneziano large-N limit. An unprecedented analysis of the CP-odd physics is performed going beyond the level of effective field theories. The structure of holographic saddle-points at finite θ is determined, as well as its interplay with chiral symmetry breaking. Many observables (vacuum energy and higher-order susceptibilities, singlet and non-singlet masses and mixings) are computed as functions of θ and the quark mass m. Wherever applicable the results are compared to those of chiral Lagrangians, finding agreement. In particular, we recover the Witten-Veneziano formula in the small x → 0 limit, we compute the θ-dependence of the pion mass and we derive the hyperscaling relation for the topological susceptibility in the conformal window in terms of the quark mass.

A holographic model of QCD in the limit of large number of colors, N c , and massless fermion flavors, N f , but constant ratio x f = N f /N c is analyzed at finite temperature and chemical potential. The five dimensional gravity model contains three bulk fields: a scalar dilaton sourcing TrF 2 , a scalar tachyon dual toqq and a 4-vector dual to the baryon currentqγ µ q. The main result is the µ, T phase diagram of the holographic theory. A first order deconfining transition along T h (µ) and a chiral transition at T χ (µ) > T h (µ) are found. The chiral transition is of second order for all µ. The dependence of thermodynamical quantities including the speed of sound and susceptibilities on the chemical potential and temperature is computed. A new quantum critical regime is found at zero temperature and finite chemical potential. It is controlled by an AdS 2 × R 3 geometry and displays semi-local criticality.

We analyze the potential of the Large Hadron Collider (LHC) to observe signatures of phenomenologically viable Walking Technicolor models. We study and compare the Drell-Yan (DY) and Vector Boson Fusion (VBF) mechanisms for the production of composite heavy vectors. We find that the heavy vectors are most easily produced and detected via the DY processes. The composite Higgs phenomenology is also studied. If Technicolor walks at the LHC its footprints will be visible and our analysis will help uncovering them.

We establish a holographic bottom-up model which covers both the baryonic and quark matter phases in cold and dense QCD. This is obtained by including the baryons using simple approximation schemes in the V-QCD model, which also includes the backreaction of the quark matter to the dynamics of pure Yang-Mills. We examine two approaches for homogeneous baryon matter: baryons as a thin layer of noninteracting matter in the holographic bulk, and baryons with a homogeneous bulk gauge field. We find that the second approach exhibits phenomenologically reasonable features. At zero temperature, the vacuum, baryon, and quark matter phases are separated by strongly first order transitions as the chemical potential varies. The equation of state in the baryonic phase is found to be stiff, i.e., the speed of sound clearly exceeds the value c 2 s = 1/3 of conformal plasmas at high baryon densities.