Abstract
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: Schrödinger isometric and warped AdS3 geometries with an SL(2, R)×U(1) isometry. We find hints of spontaneous breaking of translational symmetry, at low temperatures, around the warped backgrounds.
Highlights
Of particular interest, for example, is the existence of a colour-flavour locked phase of QCD, which is commonly known as the colour superconductivity [1], which can be characterized by a symmetry breaking: SU(3)c × SU(3)L × SU(3)R → SU(3)c+L+R
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
Summary
The general solution of (2.2)–(2.3) is hard to obtain, we will focus on a certain simple yet interesting class of solutions. Before imposing the extremal condition, at the horizon, one imposes the following conditions:. From the definition of event horizon, one obtains U (rH) = 0, V (rH) = 0 = W (rH) amounts to an overall scaling of. Imposing the extremality condition, U (rH) = 0, we can solve the resulting algebraic equations to obtain:. Demanding consistency of the solutions (i.e. imposing B2 > 0, q2 > 0 and C 2(rH) > 0), we obtain the following allowed range for the parameters, corresponding to the conditions discussed above:. We can consider the purely electric and the purely magnetic cases, in which the ChernSimons coefficient plays no role. These are the solutions that were already obtained and analyzed in [2]
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