Quantizing Open Spin Chains with Variable Length: an example from Giant Gravitons

We study an XXX open spin chain with variable number of sites, where the variability is introduced only at the boundaries. This model arises naturally in the study of Giant Gravitons in the AdS/CFT correspondence. We show how to quantize the spin chain by mapping its states to a bosonic lattice of finite length with sources and sinks of particles at the boundaries. Using coherent states, we show how the Hamiltonian for the bosonic lattice gives the correct description of semiclassical open strings ending on Giant Gravitons.Comment: 4 pages. v2: updated reference

Perturbation theory in a pure exchange non-equilibrium economy

We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We are able to show that if the economic agents have static preferences, which are also homogeneous in any of the steady states, the final wealth distribution is independent of the dynamics of the non-equilibrium theory. In particular, it is completely determined in terms of the initial conditions, and it is independent of the probability, and the network of interaction between agents. We show that the main effect of the network is to determine the relaxation time via the usual eigenvalue gap as in random walks on graphs.Comment: 7 pages, 2 figure

Consistent holographic description of boost-invariant plasma

Prior attempts to construct the gravity dual of boost-invariant flow of N=4 supersymmetric Yang-Mills gauge theory plasma suffered from apparent curvature singularities in the late time expansion. This Letter shows how these problems can be resolved by a different choice of expansion parameter. The calculations presented correctly reproduce the plasma energy-momentum tensor within the framework of second order viscous hydrodynamics.Comment: Title changed; the coordinate transformation between FG and EF coordinates elucidated; version published in PR

Sound Waves in (2+1) Dimensional Holographic Magnetic Fluids

We use the AdS/CFT correspondence to study propagation of sound waves in strongly coupled (2+1) dimensional conformal magnetic fluids. Our computation provides a nontrivial consistency check of the viscous magneto-hydrodynamics of Hartnoll-Kovtun-Muller-Sachdev to leading order in the external field. Depending on the behavior of the magnetic field in the hydrodynamic limit, we show that it can lead to further attenuation of sound waves in the (2+1) dimensional conformal plasma, or reduce the speed of sound. We present both field theory and dual supergravity descriptions of these phenomena. While to the leading order in momenta the dispersion of the sound waves obtained from the dual supergravity description agrees with the one predicted from field theory, we find a discrepancy at higher order. This suggests that further corrections to HKMS magneto-hydrodynamics are necessary.Comment: 32 pages, LaTeX; minor corrections, references added; an error in the boundary conditions fixed, a slight change in the result

Black Hole Production from High Energy Scattering in AdS/CFT

In this article we show how to set up initial states in ${\cal N} =4$ SYM theory that correspond to high energy graviton collisions, leading to black hole formation in $AdS_5\times S^5$. For this purpose, we study states in the gauge theory that are dual to graviton wavepackets localized at the center of $AdS_5$, and carrying large angular momentum along the $S^5$. These states are created by exciting only the s-wave mode of one of the complex adjoint scalars of SYM. For a single graviton, the state is 1/2 BPS and one can show that it is dual to a linearized 1/2 BPS geometry in the bulk. Exploiting this dictionary, we show how to localize the particle's wavefunciton so that the dual linearized metric has the form of a Aichelburg-Sexl shock wave. One can then put two such shock waves into a head-on collision, which is known to produce a trapped surface. Finally, we discuss the prospect of studying graviton scattering directly at strong coupling in the gauge theory using a reduced model of matrix quantum mechanics.Comment: 11 pages, revtex format, no figure

Tendency in the growth of creole kids in extensive systems

The present investigation was developed at the State of Puebla, Mexico, to describe the tendency in the growth of Creole kids by means of the evaluation of the average daily weight gain (ADWG). A total of 161 kids were controlled from the birth to the 102 days of age. Every 15 days the kids were weighed, previous fasting with separation of the mother from afternoon of the previous day. The variables included were date and weight at birth, sex, childbirth type and weights every 15 days. The results show that the average weight to the birth was 2.562 ± 0.583 kg, the males surpassing females (p<0.01) in 9.57 percent (0.232 kg). Differences were observed in favour of those of simple childbirth. The final weight was 10.186 ± 2.723 kg for the females and 11.508 ± 3.616 kg for the males. The males from simple childbirth reached a greater weight (12.229 kg). The average daily weight gain (g) for all the animals was of 82.37 ± 26.9 g. The weight at the first month reached 106.2 g; at the second 95.5 g and 53.9 g at third. The smaller gains are observed in the females born from double childbirth with 64.01 ± 17.1 g, whereas the best growth behavior was find in males from simple childbirth with 94.34 ± 30.31 g. The better adjustment of the growth was obtained with potential type equations for the total of kids (Y= 3.23X0.262); second degree polynomial equations were better for the females (Y= 3.35 + 0.07497X -0.00007085 X2); potential equations for males (Y= 4.23X0.21); and also, potential for kids of simple childbirth (Y= 3.91X0.23) and second degree polynomial equations for kids of double childbirth (Y= 3.26 + 0.0947X - 0.00002069 X2).En el Estado de Puebla, México, se desarrolló la presente investigación con el objetivo de describir la tendencia en el crecimiento de cabritos criollos mediante la evaluación de la ganancia media diaria de peso (GMDp). Se dio seguimiento individual a 161 cabritos desde el nacimiento hasta los 102 días de edad, pesándose cada 15 días, previo ayuno con separación de la madre desde la tarde del día anterior. Las variables consideradas fueron fecha y peso de nacimiento, sexo, tipo de parto y pesos quincenales. Los resultados muestran que el peso promedio al nacimiento es de 2,562 ± 0,583 kg, superando los machos a las hembras (p<0,01) en un 9,57 p.100 (0,232 kg). Los de parto simple tuvieron mejor comportamiento. El peso final fue de 10,186 ± 2,723 kg para las hembras y de 11,508 ± 3,616 kg para los machos. La ganancia media diaria de peso (g) para el total de los animales fue de 82,37 ± 26,9 g en promedio. Por períodos, al primer mes alcanzan 106,2 g; en el segundo 95,5 g y 53,9 en el tercero. Las menores ganancias se observan en las hembras nacidas de parto gemelar, con 64,01 ± 17,1 g, mientras que el mejor comportamiento lo tienen los machos simples con 94,34 ± 30,31g. Las ecuaciones de mejor ajuste del crecimiento fueron de tipo potencial para el total de cabritos (Y= 3,23X 0,262); polinomial de segundo grado para las hembras (Y= 3,35 + 0,07497X - 0,00007085X2); potencial para machos (Y= 4,23X 0,21); potencial para cabritos de parto simple (Y =3,91X 0,23) y polinomial de segundo grado para cabritos de parto doble (Y= 3,26 + 0,0947X - 0,00002069X2)

BPS Condensates, Matrix Models and Emergent String Theory

A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS condensates" which, in certain limit, have a dual description as null geodesics on the $S^5$. In the gauge theory, the condensate is similar to a representative of the chiral ring and it is described by a background of commuting matrices. Excitations around these condensates correspond to excitations around this background and take the form of "string bits" which are dual to the "giant magnons" of Hofman and Maldacena. In fact, the matrix model approach gives a {\it quantum} description of these string configurations and explains why the infinite momentum limit suppresses the quantum effects. This method allows, not only to derive part of the classical sigma model Hamiltonian of the dual string (in the infinite momentum limit), but also its quantum canonical structure. Therefore, it provides an alternative method of testing the AdS/CFT correspondence without the need of integrability.Comment: 36 pages, 1 figure, 2 appendices, v2: references adde

Integrable open spin chains from giant gravitons

We prove that in the presence of a maximal giant graviton state in N=4 SYM, the states dual to open strings attached to the giant graviton give rise to an PSU(2,2|4) open spin chain model with integrable boundary conditions in the SO(6) sector of the spin chain to one loop order.Comment: 18 pages, 2 figures, uses JHEP

A study of open strings ending on giant gravitons, spin chains and integrability

We systematically study the spectrum of open strings attached to half BPS giant gravitons in the N=4 SYM AdS/CFT setup. We find that some null trajectories along the giant graviton are actually null geodesics of AdS_5x S^5, so that we can study the problem in a plane wave limit setup. We also find the description of these states at weak 't Hooft coupling in the dual CFT. We show how the dual description is given by an open spin chain with variable number of sites. We analyze this system in detail and find numerical evidence for integrability. We also discover an interesting instability of long open strings in Ramond-Ramond backgrounds that is characterized by having a continuum spectrum of the string, which is separated from the ground state by a gap. This instability arises from accelerating the D-brane on which the strings end via the Ramond-Ramond field. From the integrable spin chain point of view, this instability prevents us from formulating the integrable structure in terms of a Bethe Ansatz construction.Comment: 38 pages+appendices, 9 figures. Uses JHEP3. v2: added reference