118376775
Young diagrams, Brauer algebras, and bubbling geometries
A bstractWe study the 1/4 BPS geometries corresponding to the 1/4 BPS operators of the dual gauge theory side, in $ \mathcal{N} = {4} $ SYM. By analyzing asymptotic structure and flux integration of the geometries, we present a mapping between droplet configurations arising from the geometries and Young diagrams of the Brauer algebra. In particular, the integer k classifying the operators in the Brauer basis is mapped to the mixing between the two angular directions.
118796950
Studies on 1/4 BPS and 1/8 BPS geometries
We analyze more explicitly four sectors of 1/4 BPS geometries and 1/8 BPS geometries, corresponding to BPS states in N=4 SYM, constructed previously. These include the states with several SO(6) angular momenta as well as those with SO(4) AdS spins. We also discuss their relations to the dual gauge theory.
15191903
Bubbling AdS space and 1/2 BPS geometries
We consider all 1/2 BPS excitations of AdS × S configurations in both type-IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. Configurations which are dual to arbitrary droplets of free fermions in phase space correspond to smooth geometries with no horizons. In fact, the ten dimensional geometry contains a special two dimensional plane which can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the collection of droplets on this plane. These solutions also give a very explicit realization of the geometric transitions between branes and fluxes. We also describe all 1/2 BPS excitations of plane wave geometries. The problem of finding the explicit geometries is reduced to solving a Laplace (or Toda) equation with simple boundary conditions. We present a large class of explicit solutions. In addition, we are led to a rather general class of AdS5 compactifications of M-theory preserving = 2 superconformal symmetry. We also find smooth geometries that correspond to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, we present a smooth 1/2 BPS solution of seven dimensional gauged supergravity corresponding to a condensate of one of the charged scalars.
118578636
Nonplanar integrability
In this article we study operators with a dimension Δ ∼ O(N) and show that simple analytic expressions for the action of the dilatation operator can be found. The operators we consider are restricted Schur polynomials. There are two distinct classes of operators that we consider: operators labeled by Young diagrams with two long columns or two long rows. The main complication in working with restricted Schur polynomials is in building a projector from a given Sn+m irreducible representation to an Sn × Sm irreducible representation (both specified by the labels of the restricted Schur polynomial). We give an explicit construction of these projectors by reducing it to the simple problem of addition of angular momentum in ordinary non-relativistic quantum mechanics. The diagonalization of the dilatation operator reduces to solving three term recursion relations. The fact that the recursion relations have only three terms is a direct consequence of the weak mixing at one loop of the restricted Schur polynomials. The recursion relations can be solved exactly in terms of symmetric Kravchuk polynomials or in terms of Clebsch-Gordan coefficients. This proves that the dilatation operator reduces to a decoupled set of harmonic oscillators and therefore it is integrable.
118812509
BPS geometry, AdS/CFT, and string theory
We first study BPS geometries dual to half-BPS states of field theories with 32 supercharges. These field theories are N = 4 SYM on R×S3, M2 brane theory and M5 brane theory. The dynamics of the half-BPS states in N = 4 SYM is reduced to a matrix quantum mechanics, and they are characterized by droplets on the two dimensional phase space. The geometries dual to these states are specified by boundary conditions on a two-plane, which are identified as the phase space. The phase space gives unified description of half-BPS perturbative and non-perturbative excitations aboveAdS5×S. The half-BPS geometries in the M theory case are described by a Toda equation with similar but more complicated boundary conditions on a two-plane. We then study BPS geometries dual to the vacua of field theories with 16 supercharges. The first class of theory has a bosonic U(1) × SO(4) × SO(4) symmetry, they include the mass deformed M2 brane theory, D4 or M5 brane theory on S3, and intersecting NS5 brane theory. Their vacua are characterized by droplets on a cylinder or torus. The second class of theory has a SU(2|4) symmetry, they include the 0+1d plane-wave matrix model, 2+1d super Yang-Mills theory on R×S2, N = 4 Super Yang-Mills on R×S/Zk, and NS5 brane theory on R× S5. The vacua of these theories are described by electrostatic configurations with many disks under external potential. The region between disks describe NS5 brane geometries. Finally we study instanton solutions and superpotentials for the vacua of the plane-wave matrix model and 2+1d super Yang-Mills theory and discuss the emergence of the vacuum geometries.
119367735
Instantons, supersymmetric vacua, and emergent geometries
We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on RxS{sup 2} with 16 supercharges. We get the superpotential in the weak-coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively, with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.
119247814
GAMMA-RAY POLARIZATION INDUCED BY COLD ELECTRONS VIA COMPTON PROCESSES
The polarization measurement is an important tool to probe the prompt emission mechanism in gamma-ray bursts (GRBs). The synchrotron photons can be scattered by cold electrons in the outflow via Compton scattering (CS) processes. The observed polarization depends on both the photon energy and the viewing angle. With the typical bulk Lorentz factor Gamma similar to 200, photons with energy E > 10 MeV tend to have smaller polarization than photons with energy E < 1 MeV. At the right viewing angle, i.e., theta similar to Gamma(-1), the polarization achieves its maximal value, and the polarization angle changes 90 degrees relative to the initial polarization direction. Thus, the synchrotron radiation plus CS model can naturally explain the 90 degrees change of the polarization angle in GRB 100826A.
119087062
Effects of iron doping on the topological insulator surfaces
Topological insulators embody a newly discovered state of matter characterized by conducting spin-momentum locked surface states that span the bulk band gap. So far, most of the study on topological insulator surfaces has been limited to understanding their properties without strong Coulomb perturbation or breaking of time reversal symmetry. We have used deposited iron, with a large positive ionization state and significant magnetic moment as a strong probe to modify the surface electronic structure of the Bi2Se3 surface at the gap energy scale. We observe that such perturbation leads to the creation of multiple Dirac fermions consistent with Z2 or Mod(2) symmetry. Taken collectively, these results are a helpful guide in manipulating topological surfaces for probing fundamental physics or developing device applications.
118473600
Galaxy Rotation Curves in the Grumiller's Modified Gravity
The effective potential in the Grumiller's modified gravity includes the Newtonian potential and a Rindler term. The fitting to the rotation curve data of eight galaxies suggests a universal Rindler acceleration a approximate to 0.30 x 10(-10) ms(-2). We do a two-parameter fit first, with the mass-to-light ratio ((sic)(*)) and the Rindler acceleration (a) as free parameters. It is found that the data of six out of the eight galaxies fit well with the prediction of theory in the range 0 r less than or similar to 40 kpc, although the theoretical curves show a tendency of arising beyond this range. The Rindler accelerations of the six well-fitted galaxies have the same magnitude, with an average value (a) over bar approximate to 0.30 x 10(-10) ms(-2). Inspired by this fact, we then carry out a one-parameter ((sic)(*)) fit to the six galaxies, with a fixed at (a) over bar, and find that the theory can still reproduce the observation. The value of Rindler acceleration we get here is a quarter of that of Milgrom's modified Newtonian dynamics. For the rest two galaxies, NGC 5055 and DDO 154, the fitting results are significantly improved if the photometric scale length (h) is included as another free parameter.
119212709
Constraining the anisotropy of the universe from supernovae and gamma-ray bursts
Recently, an anisotropic cosmological model was proposed. An arbitrary one-form, which picks out a privileged axis in the universe, was added to the Friedmann Robertson Walker (FRW) line element. The distance-redshift relation was modified such that it is direction-dependent. In this paper, we use the Union2 dataset and 59 high-redshift gamma-ray bursts (C.:411Es) to give constraints on the anisotropy of the universe. The results show that the magnitude of anisotropy is about D = 0.044 0.018, and the privileged axis points toward the direction (to, ho) = (306.1" 18.7", 18.2" 11.2') in the galactic coordinate system. The anisotropy is small and the isotropic cosmological model is an excellent approximation.
122891013
New directions in lattice gauge theory
Abstract Three topics are presented which are among those being actively explored by the RBC collaboration. In the first we extend the regularization independent renormalization scheme of the Rome-Southampton group, applying it to matrix elements computed using the Fermilab heavy quark effective action. Next we discuss the use of G-parity boundary conditions to permit the direct calculation of physical, on-shell K → ππ amplitudes. Both a theoretical description of our approach and first numerical results from studying π − π states are given. Finally, a brief summary and present status of the QCDOC project is given.