A magnetically induced quantum critical point in holography

We investigate quantum critical points in a 2+1 dimensional gauge theory at finite chemical potential χ and magnetic field B. The gravity dual is based on 4D N = 2 Fayet-Iliopoulos gauged supergravity and the solutions we consider — that are constructed analytically — are extremal, dyonic, asymptotically AdS₄ black-branes with a nontrivial radial profile for the scalar field. We discover a line of second order fixed points at B = B_c(χ) between the dyonic black brane and an extremal “thermal gas” solution with a singularity of good-type, according to the acceptability criteria of Gubser [1]. The dual field theory is a strongly coupled nonconformal field theory at finite charge and magnetic field, related to the ABJM theory [2] deformed by a triple trace operator Φ³. This line of fixed points might be useful in studying the various strongly interacting quantum critical phenomena such as the ones proposed to underlie the cuprate superconductors. We also find curious similarities between the behaviour of the VeV 〈Φ〉 under B and that of the quark condensate in 2+1 dimensional NJL models.