Scale invariance with fundamental matters and anomaly: A holographic description

Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field theory with large and arbitrary number of adjoint and fundamental degrees of freedom and a non-vanishing chiral anomaly, in the presence of an external magnetic field and with a non-vanishing density. Motivated by the richness of quantum chromodynamics under similar condition, we explore the solution space to find an infinite class of scale-invariant, but not conformal, field theories that may play a pivotal role in defining the corresponding physics. In particular, we find two classes of geometries: Schrodinger isometric and warped AdS_3 geometries with an SL(2,R) X U(1) isometry. We find hints of spontaneous breaking of translational symmetry, at low temperatures, around the warped backgrounds.