Galilean type IIA backgrounds and a map

We obtain non-relativistic AdS4 X CP3 solutions with dynamical exponent 3 in type IIA string theory, both with and without Romans mass. The compactifications to four dimensions are found to describe Proca fields in anti-de Sitter spacetime. This leads us to conclude that the massive and massless IIA theories should be identified in four dimensions and the Romans mass should be identified with the `flux' along CP3 in a definite manner. From supergravity point of view, it is suggestive of some four-dimensional symmetry that rotates Romans mass into the flux along CP3. We also provide M-theory Galilean ABJM background which gives rise to the nonrelativistic type IIA solution.Comment: 10 pages;v2: major revisions, errors on supersymmetry corrected and references added; to be published in MPL

Special limits and non-relativistic solutions

We study special vanishing horizon limit of `boosted' black D3-branes having a compact light-cone direction. The type IIB solution obtained by taking such a zero temperature limit is found to describe a nonrelativistic system with dynamical exponent 3. We discuss about such limits in M2-branes case also.Comment: 10 pages; V2: various changes in interpretations including title; no change in mathematical results, V3: minor font typo in eq.(7) remove

Doping the holographic Mott insulator

Mott insulators form because of strong electron repulsions, being at the heart of strongly correlated electron physics. Conventionally these are understood as classical "traffic jams" of electrons described by a short-ranged entangled product ground state. Exploiting the holographic duality, which maps the physics of densely entangled matter onto gravitational black hole physics, we show how Mott-insulators can be constructed departing from entangled non-Fermi liquid metallic states, such as the strange metals found in cuprate superconductors. These "entangled Mott insulators" have traits in common with the "classical" Mott insulators, such as the formation of Mott gap in the optical conductivity, super-exchange-like interactions, and form "stripes" when doped. They also exhibit new properties: the ordering wave vectors are detached from the number of electrons in the unit cell, and the DC resistivity diverges algebraically instead of exponentially as function of temperature. These results may shed light on the mysterious ordering phenomena observed in underdoped cuprates.Comment: 27 pages, 9 figures. Accepted in Nature Physic

Magnetic effects in a holographic Fermi-like liquid

We explore the magnetic properties of the Fermi-like liquid represented by the D3-D7' system. The system exhibits interesting magnetic properties such as ferromagnetism and an anomalous Hall effect, which are due to the Chern-Simons term in the effective gravitational action. We investigate the spectrum of quasi-normal modes in the presence of a magnetic field and show that the magnetic field mitigates the instability towards a striped phase. In addition, we find a critical magnetic field above which the zero sound mode becomes massive.Comment: 18 pages, 15 figure

Holographic flows to IR Lifshitz spacetimes

Recently we studied `vanishing' horizon limits of `boosted' black D3-brane geometry \cite{hsnr}. The type IIB solutions obtained by taking these special double limits were found to describe nonrelativistic Lifshitz spacetimes at zero temperature. In the present work we study these limits for TsT black-hole solutions which include $B$-field. The new Galilean solutions describe a holographic RG flow from Schr\"odinger ($a=2$) spacetime in UV to a Lifshitz universe ($a=3$) in the IR.Comment: 10 pages; v2: A bad typo in eq.8 corrected; v3: Discussion and reference on Kaigorodov spaces included, correction in sec-3, to be published in JHE

Lifshitz/Schr\"odinger D-p-branes and dynamical exponents

We extend our earlier study of special double limits of `boosted' $AdS_5$ black hole solutions to include all black D$p$-branes of type II strings. We find that Lifshitz solutions can be obtained in generality, with varied dynamical exponents, by employing these limits. We then study such double limits for `boosted' D$p$-brane bubble solutions and find that the resulting non-relativistic solutions instead describe Schr\"odinger like spacetimes, having varied dynamical exponents. We get a simple map between these Lifshitz & Schr\"odinger solutions and a relationship between two types of dynamical exponents. We also discuss about the singularities of the Lifshitz solutions and an intriguing thermodynamic duality.Comment: 20 pages; 3 figures; v3: similar to JHE

Competing orders in M-theory: superfluids, stripes and metamagnetism

We analyse the infinite class of d = 3 CFTs dual to skew-whiffed AdS 4 × SE 7 solutions of D = 11 supergravity at finite temperature and charge density and in the presence of a magnetic field. We construct black hole solutions corresponding to the unbroken phase, and at zero temperature some of these become dyonic domain walls of an Einstein-Maxwell-pseudo-scalar theory interpolating between AdS 4 in the UV and new families of dyonic AdS 2 ×R 2 solutions in the IR. The black holes exhibit both diamagnetic and paramagnetic behaviour. We analyse superfluid and striped instabilities and show that for large enough values of the magnetic field the superfluid instability disappears while the striped instability remains. For larger values of the magnetic field there is also a first-order metamagnetic phase transition and at zero temperature these black hole solutions exhibit hyperscaling violation in the IR with dynamical exponent z = 3/2 and θ = −2

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

Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

This paper focuses on supergravity duals of BPS states in N=4 super Yang-Mills. In order to describe these duals, we begin with a sequence of breathing mode reductions of IIB supergravity: first on S^3, then S^3 x S^1, and finally on S^3 x S^1 x CP^1. We then follow with a complete supersymmetry analysis, yielding 1/8, 1/4 and 1/2 BPS configurations, respectively (where in the last step we take the Hopf fibration of S^3). The 1/8 BPS geometries, which have an S^3 isometry and are time-fibered over a six-dimensional base, are determined by solving a non-linear equation for the Kahler metric on the base. Similarly, the 1/4 BPS configurations have an S^3 x S^1 isometry and a four-dimensional base, whose Kahler metric obeys another non-linear, Monge-Ampere type equation. Despite the non-linearity of the problem, we develop a universal bubbling AdS description of these geometries by focusing on the boundary conditions which ensure their regularity. In the 1/8 BPS case, we find that the S^3 cycle shrinks to zero size on a five-dimensional locus inside the six-dimensional base. Enforcing regularity of the full solution requires that the interior of a smooth, generally disconnected five-dimensional surface be removed from the base. The AdS_5 x S^5 ground state corresponds to excising the interior of an S^5, while the 1/8 BPS excitations correspond to deformations (including topology change) of the S^5 and/or the excision of additional droplets from the base. In the case of 1/4 BPS configurations, by enforcing regularity conditions, we identify three-dimensional surfaces inside the four-dimensional base which separate the regions where the S^3 shrinks to zero size from those where the S^1 shrinks.Comment: 94 pages, 6 figures, latex, typos corrected, references added, one new Appendi