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.
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.
7503241
Kac-Moody extensions of 3-algebras and M2-branes
We study the 3-algebraic structure involved in the recently shown M2-branes worldvolume gauge theories. We first extend an arbitrary finite dimensional 3-algebra into an infinite dimensional 3-algebra by adding a mode number to each generator. A unique central charge in the algebra of gauge transformations appears naturally in this extension. We present an infinite dimensional extended 3-algebra with a general metric and also a different extension with a Lorentzian metric. We then study ordinary finite dimensional 3-algebras with different signatures of the metric, focusing on the cases with a negative eigenvalue and the cases with a zero eigenvalue. In the latter cases we present a new algebra, whose corresponding theory is a decoupled abelian gauge theory together with a free theory with global gauge symmetry, and there is no negative kinetic term from this algebra.
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.
119482794
The Supergravity dual of the BMN matrix model
We propose type IIA supergravity solutions dual to the 1/2 BPS vacua of the BMN matrix model. These dual solutions are analyzed using the Polchinski-Strassler method and have brane configurations of concentric shells of D2 branes (or NS5 branes) with various radii and D0 charge. These branes can be viewed as polarized from N D0 branes by a transverse R-R magnetic 6-form flux and an NS-NS 3-form flux. In the region far from branes, the solutions reduce to perturbation around the near horizon geometry of N D0 branes, by turning on these R-R and NS-NS fluxes, which are dual to the deformation of the BFSS matrix model by adding mass terms and the Myers term. The solutions with these additional fluxes preserve 16 supersymmetries. We also briefly discuss these fluxes in the possible supergravity duals of M(atrix) theories on less supersymmetric plane-waves.
119225338
Strings on bubbling geometries
We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wave-function.
119183324
ON EXOTIC SPHERE FIBRATIONS, TOPOLOGICAL PHASES, AND EDGE STATES IN PHYSICAL SYSTEMS
We suggest that exotic sphere fibrations can be mapped to band topologies in condensed matter systems. These fibrations can correspond to geometric phases of two double bands or state vector bases with second Chern numbers m+n and -n, respectively. They can be related to topological insulators, magnetoelectric effects, and photonic crystals with special edge states. We also consider time-reversal symmetry breaking perturbations of topological insulator, and heterostructures of topological insulators with normal insulators and with superconductors. We consider periodic TI/NI/TI/NI′ heterostructures, and periodic TI/SC/TI/SC′ heterostructures. They also give rise to models of Weyl semimetals which have thermal and electrical transports.
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.
118305489
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
Recent experiments and theories have suggested that strong spin–orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic quantum-entanglement effects. Such systems feature two-dimensional surface states whose electrodynamic properties are described not by the conventional Maxwell equations but rather by an attached axion field, originally proposed to describe interacting quarks. It has been proposed that a topological insulator with a single Dirac cone interfaced with a superconductor can form the most elementary unit for performing fault-tolerant quantum computation. Here we present an angle-resolved photoemission spectroscopy study that reveals the first observation of such a topological state of matter featuring a single surface Dirac cone realized in the naturally occurring Bi_2Se_3 class of materials. Our results, supported by our theoretical calculations, demonstrate that undoped Bi_2Se_3 can serve as the parent matrix compound for the long-sought topological device where in-plane carrier transport would have a purely quantum topological origin. Our study further suggests that the undoped compound reached via n-to-p doping should show topological transport phenomena even at room temperature.
119186866
Polarization of Photons Scattered by Electrons in Any Spectral Distribution
On the basis of the quantum electrodynamics, we present a generic formalism of the polarization for beamed monochromatic photons scattered by electrons in any spectral distribution. The formulae reduce to the components of the Fano matrix when electrons are at rest. We mainly investigate the polarization in three scenarios, i.e., electrons at rest, isotropic electrons with a power-law spectrum, and thermal electrons. If the incident beam is polarized, the polarization is reduced significantly by isotropic electrons at large viewing angles; the degree of polarization caused by thermal electrons is about half of that caused by power-law electrons. If the incident bean is unpolarized, soft γ-rays can lead to about 15% polarization at viewing angles around π/4. For isotropic electrons, one remarkable feature is that the polarization as a function of the incident photon energy always peaks roughly at 1 MeV; this is valid for both the thermal and power-law cases. This feature can be used to distinguish the model of the inverse Compton scattering from that of the synchrotron radiation.
18903410
Generalized Painlevé–Gullstrand descriptions of Kerr–Newman black holes
Generalized Painlevé–Gullstrand metrics are explicitly constructed for the Kerr–Newman family of charged rotating black holes. These descriptions are free of all coordinate singularities; moreover, unlike the Doran and other proposed metrics, an extra tunable function is introduced to ensure all variables in the metrics remain real for all values of the mass $$M$$, charge $$Q$$, angular momentum $$aM$$, and cosmological constant $${\Lambda } > -\frac{3}{a^2}$$. To describe fermions in Kerr–Newman spacetimes, the stronger requirement of non-singular vierbein one-forms at the horizon(s) is imposed and coordinate singularities are eliminated by local Lorentz boosts. Other known vierbein fields of Kerr–Newman black holes are analysed and discussed; and it is revealed that some of these descriptions are actually not related by physical Lorentz transformations to the original Kerr–Newman expression in Boyer–Lindquist coordinates—which is the reason complex components appear (for certain ranges of the radial coordinate) in these metrics. As an application of our constructions the correct effective Hawking temperature for Kerr black holes is derived with the method of Parikh and Wilczek.