Notes on Properties of Holographic Matter

Probe branes with finite worldvolume electric flux in the background created by a stack of Dp branes describe holographically strongly interacting fundamental matter at finite density. We identify two quantities whose leading low temperature behavior is independent of the dimensionality of the probe branes: specific heat and DC conductivity. This behavior can be inferred from the dynamics of the fundamental strings which provide a good description of the probe branes in the regime of low temperatures and finite densities. We also comment on the speed of sound on the branes and the temperature dependence of DC conductivity at vanishing charge density.Comment: 18 pages, 2 figures; v2: corrected error in Section 6, conclusions unchanged; v3: improved figures and added clarifying comment

On-shell recursion relations for all Born QCD amplitudes

We consider on-shell recursion relations for all Born QCD amplitudes. This includes amplitudes with several pairs of quarks and massive quarks. We give a detailed description on how to shift the external particles in spinor space and clarify the allowed helicities of the shifted legs. We proof that the corresponding meromorphic functions vanish at z --> infinity. As an application we obtain compact expressions for helicity amplitudes including a pair of massive quarks, one negative helicity gluon and an arbitrary number of positive helicity gluons.Comment: 30 pages, minor change

NGN, QCD_2 and chiral phase transition from string theory

We construct a D2-D8-$\bar{D8}$ configuration in string theory, it can be described at low energy by two dimensional field theory. In the weak coupling region, the low energy theory is a nonlocal generalization of Gross-Neveu(GN) model which dynamically breaks the chiral flavor symmetry $U(N_f)_L \times U(N_f)_R$ at large $N_c$ and finite $N_f$. However, in the strong coupling region, we can use the SUGRA/Born-Infeld approximation to describe the low energy dynamics of the system. Also, we analyze the low energy dynamics about the configuration of wrapping the one direction of D2 brane on a circle with anti-periodic boundary condition of fermions. The fermions and scalars on D2 branes get mass and decouple from the low energy theory. The IR dynamics is described by the $QCD_2$ at weak coupling. In the opposite region, the dynamics has a holographic dual description. And we have discussed the phase transition of chiral symmetry breaking at finite temperature. Finally, after performing T-duality, this configuration is related to some other brane configurations.Comment: 30 pages, 3 figures, minor change

In search of the QCD-Gravity correspondence

Quantum Chromodynamics (QCD) is the fundamental theory of strong interactions. It describes the behavior of quarks and gluons which are the smallest known constituents of nuclear matter. The difficulties in solving the theory at low energies in the strongly interacting, non-perturbative regime have left unanswered many important questions in QCD, such as the nature of confinement or the mechanism of hadronization. In these lectures oriented towards the students we introduce two classes of dualities that attempt to reproduce many of the features of QCD, while making the treatment at strong coupling more tractable: (1) the AdS/CFT correspondence between a specific class of string theories and a conformal field theory and (2) an effective low-energy theory of QCD dual to classical QCD on a curved conformal gravitational background. The hope is that by applying these dualities to the evaluation of various properties of the strongly-interacting matter produced in heavy ion collisions one can understand how QCD behaves at strong coupling. We give an outline of the applications, with emphasis on two transport coefficients of QCD matter -- shear and bulk viscosities.Comment: 31 pages, 7 figures; Lectures delivered by D. Kharzeev at the International QGP Winter School, Jaipur, India, February 1-3, 200

The Random Discrete Action for 2-Dimensional Spacetime

A one-parameter family of random variables, called the Discrete Action, is defined for a 2-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this Discrete Action is calculated for various regions of 2D Minkowski spacetime. When a causally convex region of 2D Minkowski spacetime is divided into subregions using null lines the mean of the Discrete Action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to zero as the discreteness scale is taken to zero. This result is used to predict that the mean of the Discrete Action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The ``topological'' character of the Discrete Action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.Comment: 20 pages, 10 figures, Typos correcte

A note on the boundary contribution with bad deformation in gauge theory

Motivated by recently progresses in the study of BCFW recursion relation with nonzero boundary contributions for theories with scalars and fermions\cite{Bofeng}, in this short note we continue the study of boundary contributions of gauge theory with the bad deformation. Unlike cases with scalars or fermions, it is hard to use Feynman diagrams directly to obtain boundary contributions, thus we propose another method based on the ${\cal N}=4$ SYM theory. Using this method, we are able to write down a useful on-shell recursion relation to calculate boundary contributions from related theories. Our result shows the cut-constructibility of gauge theory even with the bad deformation in some generalized sense.Comment: 16 pages, 7 figure

Quantum Information Processing and Relativistic Quantum Fields

It is shown that an ideal measurement of a one-particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light-crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one-particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh-DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of field modes are shown to lead to superluminal signalling. Such detectors do, however, provide successful phenomenological models of atom-qubits interacting with quantum fields in a cavity but are valid only on time scales many orders of magnitude larger than the light-crossing time of the cavity.Comment: 16 pages, 2 figures. Improved abstract and discussion of 'ideal' measurements. References to previous work adde

Black Holes in Quasi-topological Gravity

We construct a new gravitational action which includes cubic curvature interactions and which provides a useful toy model for the holographic study of a three parameter family of four- and higher-dimensional CFT's. We also investigate the black hole solutions of this new gravity theory. Further we examine the equations of motion of quasi-topological gravity. While the full equations in a general background are fourth-order in derivatives, we show that the linearized equations describing gravitons propagating in the AdS vacua match precisely the second-order equations of Einstein gravity.Comment: 33 pages, 4 figures; two references adde

Digital sculpting for historical representation: Neville tomb case study

Despite digital 3-D polygon modelling applications providing a common and powerful tool-set for archaeological, architectural and historical visualisation over recent years, the relatively recent developments in high-resolution sculpting software allow for the possibility to create digital outcomes with a degree of surface fidelity not previously obtainable from the more widely used poly-modelling software packages. Such digital sculpting applications are more commonly applied within the video games and TV/motion picture industries, the intention of this paper is to show how such tools and methodologies together with existing scanned data and some historical knowledge can remediate and re-imagine lost sculptural form. The intended research will focus on an examination and partial re-construction of the tomb of Sir John Neville, 3rd Baron Raby located at Durham Cathedral, County Durham UK

Tree-Level Formalism

We review two novel techniques used to calculate tree-level scattering amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the MHV diagrams, we consider applications to tree-level amplitudes and focus in particular on the N=4 supersymmetric formulation. We also briefly describe the derivation of loop amplitudes using MHV diagrams. For the recursion relations, after presenting their general proof, we discuss several applications to massless theories with and without supersymmetry, to theories with massive particles, and to graviton amplitudes in General Relativity. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".Comment: 40 pages, 8 figures, invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich(ed); v2: minor corrections, references adde