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12
Interpolating from Bianchi attractors to Lifshitz and AdS spacetimes
 JHEP
, 2014
"... Abstract: We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or AdS2 × S3 geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we ..."
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Abstract: We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or AdS2 × S3 geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stressenergy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or AdS2×S3 geometries can in turn be connected to AdS5 spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to AdS5 spacetime. The asymptotic AdS5 spacetime has no nonnormalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a Cfunction can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and nonvanishing constant value at the end points. ar X iv
Stability conditions for spatially modulated phases
"... Abstract: We introduce a novel set of stability conditions for vacua with broken Lorentz symmetry. The first class of conditions require that the energy be minimized under small geometric deformations, which translates into requiring the positivity of a “stiffness ” fourtensor. The second class of ..."
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Abstract: We introduce a novel set of stability conditions for vacua with broken Lorentz symmetry. The first class of conditions require that the energy be minimized under small geometric deformations, which translates into requiring the positivity of a “stiffness ” fourtensor. The second class of conditions requires that stress forces be restoring under small deformations. We then apply these conditions to examples of recentlydiscovered spatially modulated (or “striped”) phases in holographic models of superconductors and highdensity QCD. For backreacted solutions we find that the pressure condition is equivalent to thermodynamic stability. For probe solutions, however, these conditions are in conflict with the minimization of the free energy. This suggests that either the solutions are unstable or the definition of the free energy in the probe approximation must be revised for these solutions.
Charge transport in holography with momentum dissipation
"... Abstract: In this work, we examine how charge is transported in a theory where momentum is relaxed by spatially dependent, massless scalars. We analyze the possible IR phases in terms of various scaling exponents and the (ir)relevance of operators in the IR effective holographic theory with a dilat ..."
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Abstract: In this work, we examine how charge is transported in a theory where momentum is relaxed by spatially dependent, massless scalars. We analyze the possible IR phases in terms of various scaling exponents and the (ir)relevance of operators in the IR effective holographic theory with a dilaton. We compute the (finite) resistivity and encounter broad families of (in)coherent metals and insulators, characterized by universal scaling behaviour. The optical conductivity at zero temperature and low frequencies exhibits power tails which can decay or blow up, including in the metallic regime, swamping out the contribution from the Drude peak. Their frequency scaling can differ from the resistivity scaling due to the running of the dilaton.
CHEP XXXXX Attraction, with Boundaries
"... We study the basin of attraction of static extremal black holes, in the concrete setting of the STU model. By finding a connection to a decoupled Todalike system and solving it exactly, we find a simple way to characterize the attraction basin via competing behaviors of certain parameters. The boun ..."
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We study the basin of attraction of static extremal black holes, in the concrete setting of the STU model. By finding a connection to a decoupled Todalike system and solving it exactly, we find a simple way to characterize the attraction basin via competing behaviors of certain parameters. The boundaries of attraction arise in the various limits where these parameters degenerate to zero. We find that these boundaries are generalizations of the recently introduced (extremal) subtracted geometry: the warp factors still exhibit asymptotic integer power law behaviors, but the powers can be different from one. As we cross over one of these boundaries (“generalized subttractors”), the solutions turn unstable and start blowing up at finite radius and lose their asymptotic region. Our results are fully analytic, but we also solve a simpler theory where the attraction basin is lower dimensional and easy to visualize, and present a simple picture that illustrates many of the basic ideas.
Quantum critical lines in holographic phases with (un)broken symmetry
"... Abstract: All 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 geome ..."
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Abstract: All 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 saddlepoint 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.
Contents
"... Abstract: Homogeneous, zero temperature scaling solutions with Bianchi VII spatial geometry are constructed in EinsteinMaxwellDilaton theory. They correspond to quantum critical saddle points with helical symmetry at finite density. Assuming AdS5 UV asymptotics, the small frequency/(temperature) ..."
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Abstract: Homogeneous, zero temperature scaling solutions with Bianchi VII spatial geometry are constructed in EinsteinMaxwellDilaton theory. They correspond to quantum critical saddle points with helical symmetry at finite density. Assuming AdS5 UV asymptotics, the small frequency/(temperature) dependence of the AC/(DC) electric conductivity along the director of the helix are computed. A large class of insulating and conducting anisotropic phases is found, as well as isotropic, metallic phases. Conduction can be dominated by dissipation due to weak breaking of translation symmetry or by a quantum critical current. ar X iv
Landau Levels, Anisotropy and Holography
"... We analyze properties of field theories dual to extremal black branes in (4+1) dimensions with anisotropic nearhorizon geometries. Such gravity solutions were recently shown to fall into nine classes which align with the Bianchi classification of real threedimensional Lie algebras. As a warmup we ..."
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We analyze properties of field theories dual to extremal black branes in (4+1) dimensions with anisotropic nearhorizon geometries. Such gravity solutions were recently shown to fall into nine classes which align with the Bianchi classification of real threedimensional Lie algebras. As a warmup we compute constraints on critical exponents from energy conditions in the bulk and scalar two point functions for a general type I metric, which has translation invariance but broken rotations. We also comment on the divergent nature of tidal forces in general Bianchitype metrics. Then we come to our main focus: extremal branes whose nearhorizon isometries are those of the Heisenberg algebra (type II). We find hyperscalingviolating solutions with type II isometries in (4+1)dimensions. We show that scale invariant (4+1)dimensional type II metrics are related by KaluzaKlein reduction to more symmetric AdS2 × R2 and (3+1)dimensional hyperscalingviolating spacetimes. These solutions generically have θ ≤ 0. We discuss how one can obtain flows from UV CFTs to Bianchitype spacetimes in the IR via the Higgs mechanism, as well as potential inhomogeneous instabilities of type II. Finally, we compute twopoint functions of massive and massless scalar operators in the dual field theory and find that they exhibit the behavior of a theory with Landau levels.ar X
Prepared for submission to JHEP A modulated shear to entropy ratio
"... Abstract: We study correlation functions in an equilibrated spatially modulated phase of EinsteinMaxwell twoderivative gravity. We find that the ratio of the appropriate low frequency limit of the stressstress two point function to the entropy density is modulated. The conductivity, the stresscu ..."
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Abstract: We study correlation functions in an equilibrated spatially modulated phase of EinsteinMaxwell twoderivative gravity. We find that the ratio of the appropriate low frequency limit of the stressstress two point function to the entropy density is modulated. The conductivity, the stresscurrent and currentstress correlation functions are also modulated. At temperatures close to the phase transition we obtain analytic expressions for some of the correlation functions. ar X iv