Holographic Lattices Give the Graviton an Effective Mass

We discuss the DC conductivity of holographic theories with translational invariance broken by a background lattice. We show that the presence of the lattice induces an effective mass for the graviton via a gravitational version of the Higgs mechanism. This allows us to obtain, at leading order in the lattice strength, an analytic expression for the DC conductivity in terms of the size of the lattice at the horizon. In locally critical theories this leads to a power law resistivity that is in agreement with an earlier field theory analysis of Hartnoll and Hofman.Comment: 16 pages, 2 figures, JHEP style, v2: added references. To comply with UK open access requirements, the text of the (much shorter) peer-reviewed version can be downloaded from http://www.damtp.cam.ac.uk/user/tong/pub.htm

Segmented strings coupled to a B-field

This work was supported by the Center of Mathematical Sciences and Applications at Harvard University

Adventures in Holographic Dimer Models

We abstract the essential features of holographic dimer models, and develop several new applications of these models. First, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between conventional Fermi liquids and non-Fermi liquids, accompanied by a change in the structure of the Fermi surface. Second, we make dimer vibrations propagate through the whole crystal by way of double trace deformations, obtaining nontrivial band structure. In a simple toy model, the topology of the band structure experiences an interesting reorganization as we vary the strength of the double trace deformations. Finally, we develop tools that would allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard model.Comment: 22 pages, 8 figures; v2: brief description of case of pure D5 lattice added in sec.3; v3: minor typo fixed; v4: minor change

Holographic Aspects of Fermi Liquids in a Background Magnetic Field

We study the effects of an external magnetic field on the properties of the quasiparticle spectrum of the class of 2+1 dimensional strongly coupled theories holographically dual to charged AdS$_4$ black holes at zero temperature. We uncover several interesting features. At certain values of the magnetic field, there are multiple quasiparticle peaks representing a novel level structure of the associated Fermi surfaces. Furthermore, increasing magnetic field deforms the dispersion characteristics of the quasiparticle peaks from non-Landau toward Landau behaviour. At a certain value of the magnetic field, just at the onset of Landau-like behaviour of the Fermi liquid, the quasiparticles and Fermi surface disappear.Comment: 18 pages, 10 figures. Revised some of the terminology: changed non-separable solutions to infinite-sum solution

Chaotic Strings in AdS/CFT.

Holographic theories with classical gravity duals are maximally chaotic; i.e., they saturate the universal bound on the rate of growth of chaos [J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08 (2016) 106JHEPFG1029-847910.1007/JHEP08(2016)106]. It is interesting to ask whether this property is true only for leading large N correlators or if it can show up elsewhere. In this Letter, we consider the simplest setup to tackle this question: a Brownian particle coupled to a thermal ensemble. We find that the four-point out-of-time-order correlator that diagnoses chaos initially grows at an exponential rate that saturates the chaos bound, i.e., with a Lyapunov exponent λ_{L}=2π/β. However, the scrambling time is parametrically smaller than for plasma excitations, t_{*}∼βlogsqrt[λ] instead of t_{*}∼βlogN^{2}. Our result shows that, at least in certain cases, maximal chaos can be attained in the probe sector without the explicit need of gravitational degrees of freedom.Funded by SCOAP3

Non-relativistic metrics from back-reacting fermions

It has recently been pointed out that under certain circumstances the back-reaction of charged, massive Dirac fermions causes important modifications to AdS_2 spacetimes arising as the near horizon geometry of extremal black holes. In a WKB approximation, the modified geometry becomes a non-relativistic Lifshitz spacetime. In three dimensions, it is known that integrating out charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to a gravitational and Maxwell Chern-Simons theory with a cosmological constant. Motivated by this, we look for warped AdS_3 or Schrodinger metrics as exact solutions to a fully back-reacted theory containing Dirac fermions in three and four dimensions. We work out the dynamical exponent in terms of the fermion mass and generalize this result to arbitrary dimensions.Comment: 26 pages, v2: typos corrected, references added, minor change

What If Alexander Hamilton Had Been Argentinean? A Comparison of the Early Monetary Experiences of Argentina and the United States

The contrast between the early nineteenth century Argentinean experience of high inflation and the American experience of low inflation is interpreted in terms of a dynamic monetary model of optimal taxation. It is argued that the two countries' experiences diverged because of the different constraints they faced in financing wartime government expenditures. In the presence of frequent wars, ever-tightening access to foreign capital, and an inadequate tax base, Argentina's use of the inflation tax may be viewed as an optimal solution to its wartime problems. By contrast, with the exception of the Revolutionary War, the absence of such constraints in the United States required full-tax smoothing, with only a temporary use of the inflation tax during wartime. Such policies were embodied in Alexander Hamilton's fiscal package of 1790, which allowed the United States to bond-finance most subsequent wartime expenditures.