Abstract
We investigate the combined effects of anisotropy and a magnetic field in strongly interacting gauge theories by the gauge/gravity correspondence. Our main motivation is the quark-gluon plasma produced in off-central heavy-ion collisions which exhibits large anisotropy in pressure gradients as well as large external magnetic fields. We explore two different configurations, with the anisotropy either parallel or perpendicular to the magnetic field, focusing on the competition and interplay between the two. A detailed study of the RG flow in the ground state reveals a rich structure where depending on which of the two, anisotropy or magnetic field, is stronger, intermediate geometries with approximate AdS4 × ℝ and AdS3 × ℝ2 factors arise. This competition is also manifest in the phase structure at finite temperature, specifically in the dependence of the chiral transition temperature on anisotropy and magnetic field, from which we infer the presence of inverse magnetic and anisotropic catalyses of the chiral condensate. Finally, we consider other salient observables in the theory, including the quark-antiquark potential, shear viscosity, entanglement entropy and the butterfly velocity. We demonstrate that they serve as good probes of the theory, in particular, distinguishing between the effects of the magnetic field and anisotropy in the ground and plasma states. We also find that the butterfly velocity, which codifies how fast information propagates in the plasma, exhibits a rich structure as a function of temperature, anisotropy and magnetic field, exceeding the conformal value in certain regimes.
Highlights
Studies of the quark-gluon plasma produced in heavy-ion collisions at RHIC and LHC have revealed an accepted description of this plasma as a strongly interacting relativistic fluid, see [1] for a recent review
According to the picture that emerged from these studies, the initial almond shape of the plasma created in off-central collisions leads to different pressure gradients building up in the two directions — which we denote by x1 ≡ x and x3 ≡ z, see figure 1 — that are transverse to the beam direction — which we denote by x2 ≡ y, and these different pressure gradients in turn yield different multiplicities of hadrons detected in these directions
We note that at small B, curves with nonzero a are lower than the curves with nonzero a⊥. These observations are in agreement with the idea that the inverse magnetic catalysis may be due to the anisotropy created by the magnetic field [26, 27]: the effect is stronger when the anisotropy created by the two different sources is in the same direction, and for the effect to be visible, B needs to be comparable to a
Summary
Studies of the quark-gluon plasma produced in heavy-ion collisions at RHIC and LHC have revealed an accepted description of this plasma as a strongly interacting relativistic fluid, see [1] for a recent review. One can rotate θ away by a chiral transformation, producing a constant external axial gauge field which couples to the fermions in the theory similar to the magnetic field [26] and competes with it We probe this competition between anisotropy and magnetic field by varying the value of a and B and studying the resulting effects on physical observables, i.e. the chiral transition temperature, quark-antiquark potential, string tension, entanglement entropy and the butterfly velocity. Definitions of these quantities and their holographic representations are detailed in the respective sections.
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