^{1}

^{2}

^{1}

^{3}.

We investigate QCD-like gauge theories at strong coupling at a finite magnetic field

Despite being the established theory of the strong force, the phase diagram of quantum chromodynamics is still largely unknown, especially at a finite chemical potential

Strong coupling obstructs perturbative analysis and necessitates lattice QCD studies. Indeed, lattice QCD has been an extremely fruitful method in the study of the phase diagram at a finite magnetic field

In this Letter, we take the first step in exploring this phase diagram at strong coupling using a full-fledged holographic model for QCD at a finite temperature

We model the system of strongly coupled quarks and gluons in the Veneziano limit

The gravitational solutions satisfy the first law of thermodynamics,

The phase diagram on the

We note that phase (ii), which appears only in a limited region of the phase diagram in the case

Another thermodynamic observable that is very sensitive to the phase structure is the speed of sound,

The speed of sound squared

As discussed in the Introduction, a pressing issue is the dependence of the quark condensate on the magnetic field at a finite chemical potential. One way to analyze this problem is to study the chiral transition temperature—the phase boundaries between the green or blue regions and the pink regions in Fig.

(Top panel) The chiral transition temperature

Normalizing the chiral condensate as

The normalized chiral condensate

Finally, as observed in Refs.

The magnetization divided by the magnetic field strength as a function of

There were two main results in our Letter. First was the phase diagram of a large-

Our second main result was how the region of inverse magnetic catalysis, which was observed on the lattice simulations

The choice of our model necessarily introduced a degree of arbitrariness in the particular values of thermodynamic observables. However, the main qualitative results, i.e., the generic phase diagram, the influence of

Our results were obtained by solving Einstein’s equations numerically, which is necessarily complicated since it involves backreaction of the flavor branes. To facilitate our calculations and minimize the error and the time spent, we wrote a program in

We are grateful to G. Aarts, J. O. Andersen, A. Ballon-Bayona, I. Iatrakis, A. Schmitt, and D. Zoakos for the discussions. This work was supported in part by the Netherlands Organisation for Scientific Research (NWO) under VIDI Grant No. 680-47-518, and the Delta Institute for Theoretical Physics (D-ITP), funded by the Dutch Ministry of Education, Culture and Science (OCW).

Since

For

The phase diagram at zero

The curves in this figure end on the horizontal axis at a finite

Even though the suggested lattice calculation is viable in principle, it may be plagued with technical problems, e.g., big uncertainties in the analytic continuation from imaginary to real chemical potential and a small radius of convergence even at very small values of