Landau levels in QCD

Abstract

We present first evidence for the Landau level structure of Dirac eigenmodes in full QCD for nonzero background magnetic fields, based on first principles lattice simulations using staggered quarks. Our approach involves the identification of the lowest Landau level modes in two dimensions, where topological arguments ensure a clear separation of these modes from energetically higher states, and an expansion of the full four-dimensional modes in the basis of these two-dimensional states. We evaluate various fermionic observables including the quark condensate and the spin polarization in this basis to find how much the lowest Landau level contributes to them. The results allow for a deeper insight into the dynamics of quarks and gluons in background magnetic fields and may be directly compared to low-energy models of QCD employing the lowest Landau level approximation.Comment: 21 pages, 19 figure

Improved Holographic QCD and the Quark--Gluon Plasma

“…Very recently, the question is addressed in [86] for ihQCD in the Veneziano limit (95). It is found that holography confirms, at least supports the valence vs. sea quark discussion in [94,95].…”

“…Magnetic field couples directly only to quarks in the QGP. Hence, for the same reasons as explained in section 5, its effects would be negligible in the large N c limit unless we also take N f → ∞ keeping the ratio fixed as in (95). The relevant action is the same as in that section, that is (96) with S g given by (6) and (45) and S f can be simplified down to (104) that we reproduce here:…”

“…This second source, called the "sea quarks" is weak at weak coupling compared to the first one above, hence it can be neglected, and one finds magnetic catalysis. However, it becomes stronger at intermediate or large values of the coupling constant, and it was argued in [94,95] that it dominates over the first source for relatively large values of B and T, leading to the inverse effect. These are only suggestive arguments however and it would be great to get a handle on the question in holographic QCD.…”

“…The precise physical mechanism for this behavior is not completely clear at the time of writing this review. There are indications however from further lattice studies [94,95] that this complicated profile for the condensate results from a competition between two separate sources. Considering the path integral qq one can identify these two sources as follows.…”

“…Above this transition the condensate drops to zero of course, as demonstrated by the blue curve in figure 22. The suggestion of [94,95] for the physical mechanism behind the inverse magnetic catalysis relating it to the "sea quarks" as described above can also be tested in the context of ihQCD. The two sources of coupling of the condensate to B, the direct coupling called the valence quarks, and the indirect, glue induced coupling called the sea quarks can be identified in holography with two analogous sources as sollows: The condensate is determined by solving the tachyon equation motion.…”