Spatially homogeneous Lifshitz black holes in five dimensional higher derivative gravity

We consider spatially homogeneous Lifshitz black hole solutions in five dimensional higher derivative gravity theories, which can be possible near horizon geometries of some systems that are interesting in the framework of gauge/gravity duality. We show the solutions belonging to the nine Bianchi classes in the pure R^2 gravity. We find that these black holes have zero entropy at non-zero temperatures and this property is the same as the case of BTZ black holes in new massive gravity at the critical point. In the most general quadratic curvature gravity theories, we find new solutions in Bianchi Type I and Type IX cases.Comment: 15 pages, no figure; v2, refs added, version to appear in JHE

Bosonic Fractionalisation Transitions

At finite density, charge in holographic systems can be sourced either by explicit matter sources in the bulk or by bulk horizons. In this paper we find bosonic solutions of both types, breaking a global U(1) symmetry in the former case and leaving it unbroken in the latter. Using a minimal bottom-up model we exhibit phase transitions between the two cases, under the influence of a relevant operator in the dual field theory. We also embed solutions and transitions of this type in M-theory, where, holding the theory at constant chemical potential, the cohesive phase is connected to a neutral phase of Schr\"odinger type via a z=2 QCP.Comment: references added. minor changes. version published in JHE

Axion monodromy in a model of holographic gluodynamics

The low energy field theory for N type IIA D4-branes at strong 't Hooft coupling, wrapped on a circle with antiperiodic boundary conditions for fermions, is known to have a vacuum energy which depends on the $\theta$ angle for the gauge fields, and which is a multivalued function of this angle. This gives a field-theoretic realization of "axion monodromy" for a nondynamical axion. We construct the supergravity solution dual to the field theory in the metastable state which is the adiabatic continuation of the vacuum to large values of $\theta$. We compute the energy of this state and show that it initially rises quadratically and then flattens out. We show that the glueball mass decreases with $\theta$, becoming much lower than the 5d KK scale governing the UV completion of this model. We construct two different classes of domain walls interpolating between adjacent vacua. We identify a number of instability modes -- nucleation of domain walls, bulk Casimir forces, and condensation of tachyonic winding modes in the bulk -- which indicate that the metastable branch eventually becomes unstable. Finally, we discuss two phenomena which can arise when the axion is dynamical; axion-driven inflation, and axion strings.Comment: 43 pages, 10 figures. v2: references update

Universality and exactness of Schrodinger geometries in string and M-theory

We propose an organizing principle for classifying and constructing Schrodinger-invariant solutions within string theory and M-theory, based on the idea that such solutions represent nonlinear completions of linearized vector and graviton Kaluza-Klein excitations of AdS compactifications. A crucial simplification, derived from the symmetry of AdS, is that the nonlinearities appear only quadratically. Accordingly, every AdS vacuum admits infinite families of Schrodinger deformations parameterized by the dynamical exponent z. We exhibit the ease of finding these solutions by presenting three new constructions: two from M5 branes, both wrapped and extended, and one from the D1-D5 (and S-dual F1-NS5) system. From the boundary perspective, perturbing a CFT by a null vector operator can lead to nonzero beta-functions for spin-2 operators; however, symmetry restricts them to be at most quadratic in couplings. This point of view also allows us to easily prove nonrenormalization theorems: for any Sch(z) solution of two-derivative supergravity constructed in the above manner, z is uncorrected to all orders in higher derivative corrections if the deforming KK mode lies in a short multiplet of an AdS supergroup. Furthermore, we find infinite classes of 1/4 BPS solutions with 4-,5- and 7-dimensional Schrodinger symmetry that are exact.Comment: 31 pages, plus appendices; v2, minor corrections, added refs, slight change in interpretation in section 2.3, new Schrodinger and Lifshitz solutions included; v3, clarifications in sections 2 and 3 regarding existence of solutions and multi-trace operator

Shear Modes, Criticality and Extremal Black Holes

We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential fixed.Comment: 28 pages, 7 figures, added reference

Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure

We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we study the causal structure by probing the space-time with point particles as well as with scalar fields. We show that, even though there is no global time function in the technical sense (Schroedinger space-time being non-distinguishing), the time coordinate of the global Schroedinger coordinate system is, in a precise way, the closest one can get to having such a time function. In spite of this and the corresponding strongly Galilean and almost pathological causal structure of this space-time, it is nevertheless possible to define a Hilbert space of normalisable scalar modes with a well-defined time-evolution. We also discuss how the Galilean causal structure is reflected and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page

Quantum critical lines in holographic phases with (un)broken symmetry

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 saddle-point solutions are characterized by three critical exponents ($\theta, z, \zeta$). 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.Comment: v3: 32+29 pages, 2 figures. Matches version published in JHEP. Important addition of an exponent characterizing the IR scaling of the electric potentia

On nonsupersymmetric \BC^4/\BZ_N, tachyons, terminal singularities and flips

We investigate nonsupersymmetric \BC^4/\BZ_N orbifold singularities using their description in terms of the string worldsheet conformal field theory and its close relation with the toric geometry description of these singularities and their possible resolutions. Analytic and numerical study strongly suggest the absence of nonsupersymmetric Type II terminal singularities (i.e. with no marginal or relevant blowup modes) so that there are always moduli or closed string tachyons that give rise to resolutions of these singularities, although supersymmetric and Type 0 terminal singularities do exist. Using gauged linear sigma models, we analyze the phase structure of these singularities, which often involves 4-dimensional flip transitions, occurring between resolution endpoints of distinct topology. We then discuss 4-dim analogs of unstable conifold-like singularities that exhibit flips, in particular their Type II GSO projection and the phase structure. We also briefly discuss aspects of M2-branes stacked at such singularities and nonsupersymmetric AdS_4\times S^7/\BZ_N backgrounds.Comment: Latex, 43pgs incl. appendices, 2 eps figs, v2. minor clarifications added, to appear in JHE

Conductivity and quasinormal modes in holographic theories

We show that in field theories with a holographic dual the retarded Green's function of a conserved current can be represented as a convergent sum over the quasinormal modes. We find that the zero-frequency conductivity is related to the sum over quasinormal modes and their high-frequency asymptotics via a sum rule. We derive the asymptotics of the quasinormal mode frequencies and their residues using the phase-integral (WKB) approach and provide analytic insight into the existing numerical observations concerning the asymptotic behavior of the spectral densities.Comment: 24 pages, 3 figure