Understanding the Random Displacement Model: From Ground-State Properties to Localization

We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.Comment: 31 pages, 7 figures, final version, to appear in Proceedings of "Spectral Days 2010", Santiago, Chile, September 20-24, 201

Massive Quantum Liquids from Holographic Angel's Trumpets

We explore the small-temperature regime in the deconfined phase of massive fundamental matter at finite baryon number density coupled to the 3+1 dimensional N=4 SYM theory. In this setting, we can demonstrate a new type of non-trivial temperature-independent scaling solutions for the probe brane embeddings. Focusing mostly on matter supported in 2+1 dimensions, the thermodynamics indicate that there is a quantum liquid with interesting density-dependent low-temperature physics. We also comment about 3+1 and 1+1 dimensional systems, where we further find for example a new thermodynamic instability.Comment: 18+1 pages, 6 figures; replaced fig. 6 and comments in sec. 5.2; minor explanations added and typos fixed, final version published in JHEP (modulo fig. 3); factor of \sqrt{\lambda} and corresponding comments fixe

Holographic Approach to Regge Trajectory and Rotating D5 brane

We study the Regge trajectories of holographic mesons and baryons by considering rotating strings and D5 brane, which is introduced as the baryon vertex. Our model is based on the type IIB superstring theory with the background of asymptotic $AdS_5\times S^5$. This background is dual to a confining supersymmetric Yang-Mills theory (SYM) with gauge condensate, $$, which determines the tension of the linear potential between the quark and anti-quark. Then the slope of the meson trajectory ($\alpha'_{M}$) is given by this condensate as $\alpha'_{M}=1/\sqrt{\pi }$ at large spin $J$. This relation is compatible with the other theoretical results and experiments. For the baryon, we show the importance of spinning baryon vertex to obtain a Regge slope compatible with the one of $N$ and $\Delta$ series. In both cases, mesons and baryons, the trajectories are shifted to large mass side with the same slope for increasing current quark mass.Comment: 28 pages, 7 figure

Physical Response Functions of Strongly Coupled Massive Quantum Liquids

We study physical properties of strongly coupled massive quantum liquids from their spectral functions using the AdS/CFT correspondence. The generic model that we consider is dense, heavy fundamental matter coupled to SU(N_c) super Yang-Mills theory at finite temperature above the deconfinement phase transition but below the scale set by the baryon number density. In this setup, we study the current-current correlators of the baryon number density using new techniques that employ a scaling behavior in the dual geometry. Our results, the AC conductivity, the quasi-particle spectrum and the Drude-limit parameters like the relaxation time are simple temperature-independent expressions that depend only on the mass-squared to density ratio and display a crossover between a baryon- and meson-dominated regime. We concentrated on the (2+1)-dimensional defect case, but in principle our results can also be generalized straightforwardly to other cases.Comment: 21 pages, 10 figures, extra paragraph and figure are added in response to referee's comment

Rigidity of SU(2,2|2)-symmetric solutions in Type IIB

We investigate the existence of half-BPS solutions in Type IIB supergravity which are invariant under the superalgebra SU(2,2|2) realized on either AdS_5 x S^2 x S^1 or AdS_5 x S^3 warped over a Riemann surface \Sigma with boundary. We prove that, in both cases, the only solution is AdS_5 x S^5 itself. We argue that this result provides evidence for the non-existence of fully back-reacted intersecting D3/D7 branes with either AdS_5 x S^2 x S^1 x \Sigma or AdS_5 x S^3 x \Sigma near-horizon limits.Comment: 55 page

Complementary cooperation, minimal winning coalitions, and power indices

We introduce a new simple game, which is referred to as the complementary weighted multiple majority game (C-WMMG for short). C-WMMG models a basic cooperation rule, the complementary cooperation rule, and can be taken as a sister model of the famous weighted majority game (WMG for short). In this paper, we concentrate on the two dimensional C-WMMG. An interesting property of this case is that there are at most $n+1$ minimal winning coalitions (MWC for short), and they can be enumerated in time $O(n\log n)$, where $n$ is the number of players. This property guarantees that the two dimensional C-WMMG is more handleable than WMG. In particular, we prove that the main power indices, i.e. the Shapley-Shubik index, the Penrose-Banzhaf index, the Holler-Packel index, and the Deegan-Packel index, are all polynomially computable. To make a comparison with WMG, we know that it may have exponentially many MWCs, and none of the four power indices is polynomially computable (unless P=NP). Still for the two dimensional case, we show that local monotonicity holds for all of the four power indices. In WMG, this property is possessed by the Shapley-Shubik index and the Penrose-Banzhaf index, but not by the Holler-Packel index or the Deegan-Packel index. Since our model fits very well the cooperation and competition in team sports, we hope that it can be potentially applied in measuring the values of players in team sports, say help people give more objective ranking of NBA players and select MVPs, and consequently bring new insights into contest theory and the more general field of sports economics. It may also provide some interesting enlightenments into the design of non-additive voting mechanisms. Last but not least, the threshold version of C-WMMG is a generalization of WMG, and natural variants of it are closely related with the famous airport game and the stable marriage/roommates problem.Comment: 60 page

Dynamics of the chiral phase transition from AdS/CFT duality

We use Lorentzian signature AdS/CFT duality to study a first order phase transition in strongly coupled gauge theories which is akin to the chiral phase transition in QCD. We discuss the relation between the latent heat and the energy (suitably defined) of the component of a D-brane which lies behind the horizon at the critical temperature. A numerical simulation of a dynamical phase transition in an expanding, cooling Quark-Gluon plasma produced in a relativistic collision is carried out.Comment: 30 pages, 5 figure

Holographic Roberge-Weiss Transitions

We investigate N=4 SYM coupled to fundamental flavours at nonzero imaginary quark chemical potential in the strong coupling and large N limit, using gauge/gravity duality applied to the D3-D7 system, treating flavours in the probe approximation. The interplay between Z(N) symmetry and the imaginary chemical potential yields a series of first-order Roberge-Weiss transitions. An additional thermal transition separates phases where quarks are bound/unbound into mesons. This results in a set of Roberge-Weiss endpoints: we establish that these are triple points, determine the Roberge-Weiss temperature, give the curvature of the phase boundaries and confirm that the theory is analytic in mu^2 when mu^2~0.Comment: 37 pages, 13 figures; minor comments added, to appear in JHE

Pion and Vector Meson Form Factors in the Kuperstein-Sonnenschein holographic model

We study phenomenological aspects of the holographic model of chiral symmetry breaking recently introduced by Kuperstein and Sonnenschein (KS). As a first step, we calculate the spectrum of vector and axial-vector mesons in the KS model. We numerically compute various coupling constants of the mesons and pions. Our analysis indicates that vector meson dominance is realized in this model. The pion, vector meson and axial-vector meson form factors are obtained and studied in detail. We find good agreement with QCD results. In particular, the pion form factor closely matches available experimental data.Comment: v1: 27 pages, 9 figures, 4 tables; v2: minor changes, added more general discussion of vector meson dominance; v3: minor changes and additions, version accepted for publication in JHE