Collective excitations of holographic quantum liquids in a magnetic field
Abstract
We use holography to study {N} = 4 supersymmetric SU( N _{c}) YangMills theory in the large N _{c} and largecoupling limits coupled to a number N _{ f } ≪ N _{ c } of ( n + 1)dimensional massless supersymmetric hypermultiplets in the fundamental representation of SU(Nc), with n = 2, 3. We introduce a temperature T, a baryon number chemical potential μ, and a baryon number magnetic field B, and work in a regime with μ ≫ T, √{B} . We study the collective excitations of these holographic quantum liquids by computing the poles in the retarded Green's function of the baryon number charge density operator and the associated peaks in the spectral function. We focus on the evolution of the collective excitations as we increase the frequency relative to T , i.e. the hydrodynamic/collisionless crossover. We find that for all B, at low frequencies the tallest peak in the spectral function is associated with hydrodynamic charge diffusion. At high frequencies the tallest peak is associated with a sound mode similar to the zero sound mode in the collisionless regime of a Landau Fermi liquid. The sound mode has a gap proportional to B, and as a result for intermediate frequencies and for B sufficiently large compared to T the spectral weight is strongly suppressed. We find that the hydrodynamic/collisionless crossover occurs at a frequency that is approximately Bindependent.
 Publication:

Journal of High Energy Physics
 Pub Date:
 November 2012
 DOI:
 10.1007/JHEP11(2012)084
 arXiv:
 arXiv:1209.0009
 Bibcode:
 2012JHEP...11..084B
 Keywords:

 Dbranes;
 Holography and condensed matter physics (AdS/CMT);
 High Energy Physics  Theory
 EPrint:
 45 pages, 8 png and 47 pdf images in 22 figures