QCD vacuum properties in a magnetic field from AdS/CFT: chiral condensate and Goldstone mass

Abstract

Chiral condensate and η ′ meson mass spectrum are studied under the influence of an external Abelian magnetic field. We work within the D3/D7 Karch-Katz model of flavoured AdS/CFT with supersymmetry broken by the Constable-Myers deformation of the metric. It is shown that this setting yields an analytic (quadratic) dependence of condensate on field, typical for the Nambu-Jona-Lasinio model, rather than the nonanalytic (linear in field) result, typical for chiral perturbation theory in the exact chiral limit. We conjecture that the analytic (quadratic) result might be put into correspondence with the leading-order in the 1/N c decomposition for the condensate. This leading order in the 1/N c approximation has not yet been derived from the chiral perturbation theory. Thus the dual model yields the quadratic field dependence of the condensate, which is beyond the range of feasibility of chiral perturbation theory.

Non-equilibrium physics at a holographic chiral phase transition

“…At small B the system is in the symmetric phase (c = 0). The tendency for the condensate to increase with B is in qualitative agreement with observations in chiral perturbation theory [38,39] (∝ B 3/2 for strong fields, ∝ B for weak fields), in the Nambu-Jona-Lasinio model [40] (∝ B 2 ), in a confining deformation of the holographic Karch-Katz model [19] (∝ B 2 ), and in SU(2) [41] (∝ B) and SU(3) [42] lattice calculations (∝ B 1.6±0.2 ). The dependence on B typically ranges from linear to quadratic behaviour, i.e.…”

“…Several mechanisms for triggering this condensation have been explored. The cleanest is when a background magnetic field is introduced [15][16][17][18][19][20][21][22][23] so we will use that mechanism here. The reader might want to loosely view the B field as simply the introduction of a conformal symmetry and supersymmetry breaking parameter that triggers the strong dynamics to cause the symmetry breaking.…”

“…Knowing the explicit background geometry (2.9) we can study flavour physics using the D7 brane DBI action. The action schematically reads 19) where A and B are complicated but known functions of τ and ρ, see (3.5) and (3.6) …”

Improved Holographic QCD and the Quark--Gluon Plasma

“…Note that this term in the action is suppressed as 1/N 2 c compared to the two terms in (96) consistently with the fact that the physics associated with the dual operator (147) in QCD is 1/N 2 c suppressed in the large-N limit. Practically this means that we do not take into account the backreaction of (152) on the background that results from (96) this the field a(r, x) can be treated as a perturbation on top of the ihQCD background obtained in the previous sections.…”

“…The question has been addressed in the various papers in holography [96,97,98,99,100,101,102,103], or with smeared backreacted flavor branes in the Veneziano limit [104] but most of these works are either for adjoint flavors or consider small values of fundamental quarks. Very recently, the question is addressed in [86] for ihQCD in the Veneziano limit (95).…”