Abstract
AbstractAll possible scaling IR asymptotics in homogeneous, translation invariant holographic phases preserving or breaking a U(1) symmetry in the IR are classified. Scale invariant geometries where the scalar extremizes its effective potential are distinguished from hyperscaling violating geometries where the scalar runs logarithmically. It is shown that the general critical saddle-point solutions are characterized by three critical exponents (θ, z, ζ). Both exact solutions as well as leading behaviors are exhibited. Using them, neutral or charged geometries realizing both fractionalized or cohesive phases are found. The generic global IR picture emerging is that of quantum critical lines, separated by quantum critical points which correspond to the scale invariant solutions with a constant scalar.
Highlights
Effective holographic theories (EHTs) and their parametrization have been advocated as a useful and powerful tool to analyze the phase structure of holographic strongly coupled theories following the Wilsonian philosophy and classify all universality classes of holographic critical behavior, [1]
The generic global IR picture emerging is that of quantum critical lines, separated by quantum critical points which correspond to the scale invariant solutions with a constant scalar
This is independent of whether we are in U(1)-preserving/violating, cohesive/fractionalized phases. This distinction between fractionalized and cohesive phases has been tied to a specific kind of quantum phase transitions describing the onset of fractionalisation, [38,39,40]. They involve a scale invariant IR quantum critical point, which sits at a bifurcation in the holographic RG flow, see figure 1
Summary
Effective holographic theories (EHTs) and their parametrization have been advocated as a useful and powerful tool to analyze the phase structure of holographic strongly coupled theories following the Wilsonian philosophy and classify all universality classes of holographic (quantum) critical behavior, [1]. The charged degrees of freedom outside the extremal horizon do not source any electric flux in the deep IR and are dual to “confined” gauge-invariant operators: they realize cohesive phases By considering both exact and power series solutions, we are able to accommodate cohesive and fractionalized phases both, with a single scalar field. They involve a scale invariant IR quantum critical point, which sits at a bifurcation in the holographic RG flow (that is, it has both a relevant and an irrelevant perturbation), see figure 1 As it is unstable, this IR fixed point can only be reached from the UV boundary at the price of fine-tuning the sole dimensionless coupling of the boundary theory, g = gO/μ, where μ is the chemical and gO the coupling for the operator O dual to the bulk scalar field responsible for driving the IR asymptotics. This comparison suggests that the T → 0 limit of cuprates, in the overdoped phase, may be described by a quantum critical line, [37]
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