Holographic magnetic susceptibility

Abstract

The (2+1)-dimensional static magnetic susceptibility in strong-coupling is studied via a Reissner-Nordström-AdS geometry. The analyticity of the susceptibility on the complex momentum q-plane in relation to the Friedel-like oscillation in coordinate space is explored. In contrast to the branchcuts crossing the real momentum-axis for a Fermi liquid, we prove that the holographic magnetic susceptibility remains an analytic function of the complex momentum around the real axis in the limit of zero temperature. At zero temperature, we located analytically two pairs of branch-cuts that are parallel to the imaginary momentum-axis for large |Im q| but become warped with the end-points keeping away from the real and imaginary momentum-axes. We conclude that these branch-cuts give rise to the exponential decay behaviour of Friedel-like oscillation of magnetic susceptibility in coordinate space. We also derived the analytical forms of the susceptibility in large and small-momentum, respectively.

Study on a holographic static transverse polarization at non-zero temperature

“…The small momentum expansion for C yy (q) is studies in Ref. [13], the key steps is to find the explicit expressions of åy (q) and å y (q) by not solving the Eqns. (9)(10) directly, but via expanding the master-field equation in term of the momentum in order to obtain a pair of inhomogeneous equations, see Eqn.…”

“…We shall consider the solutions of the linearized Einstein-Maxwell equations as the first order fluctuation, more details shown in [14] and [13], for our main purpose, the below coupled differential equations will be explored:…”

“…Because of the analytical work in Ref. [13], we have a comparison to tell the validity of our computation. In small momentum expansion, it's proven that C yy (q) is an analytic function along the real-axis, and shows…”

“…In the work [13], we further studied the explicit expressions of static transverse polarization on both small and large momentum expansion. It's proven that the strongly-coupled polarization is a meoromorphic function of momentum at T = 0; and at T = 0, all simple poles condensate together and form a pair of branch-cuts, this pattern is very different with ones in weakly-coupled counterpart.…”

The noncommutativity of the static and homogeneous limit of the axial chemical potential in chiral magnetic effect

“…But the lattice simulation indicates a nonzero magnetic mass of gluons [32][33][34], which serves an infrared cutoff. In addition, a recent calculation based on holography shows that such a noncommutativity stays in strongly coupled N = 4 super Yang-Mills theory [35].…”