Towards a Realization of the Condensed-Matter/Gravity Correspondence in String Theory via Consistent Abelian Truncation

We present an embedding of the 3-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an $\mathcal{N}=6$, $U(N)\times U(N)$ Chern-Simons-matter theory (the ABJM model) by consistently truncating the latter to an abelian effective field theory encoding the collective dynamics of ${\cal O}(N)$ of the ${\cal O}(N^2)$ modes. In fact, depending on the VEV on one of the ABJM scalars, a mass deformation parameter $\mu$ and the Chern-Simons level number $k$, our abelianization prescription allows us to interpolate between the abelian Higgs model with its usual multi-vortex solutions and a $\phi^4$ theory. We sketch a simple condensed matter model that reproduces all the salient features of the abelianization. In this context, the abelianization can be interpreted as giving a dimensional reduction from four dimensions.Comment: 4 pages, revtex; reference added, typo corrected; added clarifying paragraphs at end of introduction and on pages 3-4. Version accepted to PR

Diffusion in an Expanding Plasma using AdS/CFT

We consider the diffusion of a non-relativistic heavy quark of fixed mass M, in a one-dimensionally expanding and strongly coupled plasma using the AdS/CFT duality. The Green's function constructed around a static string embedded in a background with a moving horizon, is identified with the noise correlation function in a Langevin approach. The (electric) noise decorrelation is of order 1/T(\tau) while the velocity de-correlation is of order MD(\tau)/T(\tau). For MD>1, the diffusion regime is segregated and the energy loss is Langevin-like. The time dependent diffusion constant D(\tau) asymptotes its adiabatic limit 2/\pi\sqrt{\lambda} T(\tau) when \tau/\tau_0=(1/3\eta_0\tau_0)^3 where \eta_0 is the drag coefficient at the initial proper time \tau_0.Comment: 19 pages, 2 figures, minor corrections, version to appear in JHE

Abelian-Higgs and Vortices from ABJM: towards a string realization of AdS/CMT

We present ans\"{a}tze that reduce the mass-deformed ABJM model to gauged Abelian scalar theories, using the fuzzy sphere matrices $G^\alpha$. One such reduction gives a Toda system, for which we find a new type of nonabelian vortex. Another gives the standard Abelian-Higgs model, thereby allowing us to embed all the usual (multi-)vortex solutions of the latter into the ABJM model. By turning off the mass deformation at the level of the reduced model, we can also continuously deform to the massive $\phi^4$ theory in the massless ABJM case. In this way we can embed the Landau-Ginzburg model into the AdS/CFT correspondence as a consistent truncation of ABJM. In this context, the mass deformation parameter $\mu$ and a field VEV $$ act as $g$ and $g_c$ respectively, leading to a well-motivated AdS/CMT construction from string theory. To further this particular point, we propose a simple model for the condensed matter field theory that leads to an approximate description for the ABJM abelianization. Finally, we also find some BPS solutions to the mass-deformed ABJM model with a spacetime interpretation as an M2-brane ending on a spherical M5-brane.Comment: 43 pages, latex, explanations added in the introduction, end of section 4, and on page 2

Quark-Gluon Plasma/Black Hole duality from Gauge/Gravity Correspondence

The Quark-Gluon Plasma (QGP) is the QCD phase of matter expected to be formed at small proper-times in the collision of heavy-ions at high energy. Experimental observations seem to favor a strongly coupled QCD plasma with the hydrodynamic properties of a quasi-perfect fluid, i.e. rapid thermalization (or isotropization) and small viscosity. The theoretical investigation of such properties is not obvious, due to the the strong coupling. The Gauge/Gravity correspondence provides a stimulating framework to explore the strong coupling regime of gauge theories using the dual string description. After a brief introduction to Gauge/Gravity duality, and among various existing studies, we focus on challenging problems of QGP hydrodynamics, such as viscosity and thermalization, in terms of gravitational duals of both the static and relativistically evolving plasma. We show how a Black Hole geometry arises naturally from the dual properties of a nearly perfect fluid and explore the lessons and prospects one may draw for actual heavy ion collisions from the Gauge/Gravity duality approach.Comment: 6 pages, 4 figures, invited talk at the EPS HEP 2007 Conference, Manchester (UK), and at the ``Deuxiemes rencontres PQG-France'', Etretat (2007); reference adde

A Trouble with Ho\v{r}ava-Lifshitz Gravity

We study the structure of the phase space in Ho\v{r}ava-Lifshitz theory. With the constraints derived from the action, the phase space is described by five fields, thus there is a lack of canonical structure. The Poisson brackets of the Hamiltonian density do not form a closed structure, resulting in many new constraints. Taking these new constraints into account, it appears that there is no degree of freedom left, or the phase space is reduced to one with an odd number of fields.Comment: 12 pages, some discussions, comments and references added, JHEP styl

Correspondence principle for a brane in Minkowski space and vector mesons

We consider a 3-brane of positive cosmological constant (de Sitter) in D-dimensional Minkowski space. We show that the Poincare algebra in the bulk yields a SO(4,2) algebra when restricted to the brane. In the limit of zero cosmological constant (flat brane), this algebra turns into the conformal algebra on the brane. We derive a correspondence principle for Minkowski space analogous to the AdS/CFT correspondence. We discuss explicitly the cases of scalar and gravitational fields. For a 3-brane of finite thickness in the transverse directions, we obtain a spectrum for vector gravitational perturbations which correspond to vector mesons. The spectrum agrees with the one obtained in truncated AdS space by de Teramond and Brodsky provided D=10 and the bulk mass scale M is of order the geometric mean of the Planck mass ($\bar M$) on the brane and $\Lambda_{QCD}$ ($M \sim (\bar M \Lambda_{QCD})^{1/2} \sim 10^9$ GeV).Comment: 8 pages in two-column ReVTeX

Five-dimensional SYM from undeformed ABJM

We expand undeformed ABJM theory around the vacuum solution that was found in arxiv:0909.3101. This solution can be interpreted as a circle-bundle over a two-dimensional plane with a singularity at the origin. By imposing periodic boundary conditions locally far away from the singularity, we obtain a local fuzzy two-torus over which we have a circle fibration. By performing fluctuation analysis we obtain five-dimensional SYM with the precise value on the coupling constant that we would obtain by compactifying multiple M5 branes on the vacuum three-manifold. In the resulting SYM theory we also find a coupling to a background two-form.Comment: 23 page

Taxonomy Induction using Hypernym Subsequences

We propose a novel, semi-supervised approach towards domain taxonomy induction from an input vocabulary of seed terms. Unlike all previous approaches, which typically extract direct hypernym edges for terms, our approach utilizes a novel probabilistic framework to extract hypernym subsequences. Taxonomy induction from extracted subsequences is cast as an instance of the minimumcost flow problem on a carefully designed directed graph. Through experiments, we demonstrate that our approach outperforms stateof- the-art taxonomy induction approaches across four languages. Importantly, we also show that our approach is robust to the presence of noise in the input vocabulary. To the best of our knowledge, no previous approaches have been empirically proven to manifest noise-robustness in the input vocabulary

Hyperbolic fracton model, subsystem symmetry, and holography. II. The dual eight-vertex model

The discovery of fracton states of matter opens up an exciting, largely unexplored field of many-body physics. Certain fracton states\u27 similarity to gravity is an intriguing property. In an earlier work [Phys. Rev. B 99, 155126 (2019)], we have demonstrated that a simple fracton model in anti-de Sitter space satisfies several major holographic properties. In this follow-up paper, we study the eight-vertex model dual to the original model. The dual model has the advantage of illuminating the mutual information and subsystem charges pictorially, which helps to reveal its connections to various other topics in the study of holography and fracton phases. At zero temperature, the dual eight-vertex model is a discrete realization of the bit-thread model, a powerful tool developed to visualize holography. The bit-thread picture combined with subsystem charges can give a quantitative account of the isometry between the bulk and the boundary at finite energy, which is also a key issue for holography. The black hole microscopic degrees of freedom can be identified in this picture, which turn out to be encoded nonlocally on the horizon. The eight-vertex model proves to be a very helpful venue to improve our understanding of the hyperbolic fracton model as a toy model of holography