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.
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.
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.
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.
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.
6410332
Fivebranes from gauge theory
We study theories with 16 supercharges and a discrete energy spectrum. One class of theories has symmetry group SU(2|4). They arise as truncations of N=4 super Yang-Mills theory. They include the plane-wave matrix model, 2+1 super Yang-Mills theory on RxS{sup 2} and N=4 super Yang-Mills theory on RxS{sup 3}/Z{sub k}. We explain how to obtain their gravity duals in a unified way. We explore the regions of the geometry that are relevant for the study of some 1/2 BPS and near BPS states. This leads to a class of two dimensional (4,4) supersymmetric sigma models with nonzero H flux, including a massive deformed WZW model. We show how to match some features of the string spectrum with the Yang-Mills theory. The other class of theories are also connected to N=4 super Yang-Mills theory and arise by making some of the transverse scalars compact. Their vacua are characterized by a 2D Yang-Mills theory or 3D Chern-Simons theory. These theories realize peculiar super-Poincare symmetry algebras in 2+1 or 1+1 dimensions with ''noncentral'' charges. We finally discuss gravity duals of N=4 super Yang-Mills theory on AdS{sub 3}xS{sup 1}.
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.
119207380
GAMMA-RAY BURST POLARIZATION VIA COMPTON SCATTERING PROCESS
Synchrotron radiation and Compton scattering are widely accepted as the most likely emission mechanisms of some astrophysical phenomena, such as gamma-ray bursts (GRBs) and active galactic nuclei. The measurement of the polarization of photons provides a useful tool to distinguish different emission mechanisms and structures of the emission region. Based on the differential cross section of a polarized photon scattered by an unpolarized electron of any initial momentum, we derive an analytical formula of polarization for beamed photons scattered by isotropic electrons with a power-law distribution. Numerical calculations are carried out in four special cases: electrons at rest, Thomson limit, head-on collision, and monochromatic electrons. It is found that the maximum polarization can be as high as 100% for low energy photons, if the electrons are at rest. Although polarization is highly suppressed due to the isotropic electrons, a maximum value of similar to 10%-20% can still be achieved. The Compton scattering process can be used to explain the polarization of GRB 041219A and GRB 100826A.
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.
55602833
A new platform for topological quantum phenomena : Topological Insulator states in thermoelectric Heusler-related ternary compounds
Topological insulators (TI) realize a novel state of quantum matter that are distinguished by topological invariants of bulk band structure rather than spontaneously broken symmetries. A number of exotic quantum phenomena have been predicted to exist in multiply-connected geometries which require an enormous amount of materials flexibility. We have extended our previous search for TI materials from binary (Bi2X3 series) to the thermoelectric ternary compounds. We discover that the distorted LuPtSb is the first ternary compound harboring a 3D topological insulator state. We also show that the half-Heusler LuPtSb-type series is a natural platform that hosts a range of candidate compounds, alloys and artificial heterostructures (quantum-wells). We also discovered several different paradigms of trivial and non-trivial topological ordering in this class, including a metallic nontrivial topological state in YAuPb. Some of these materials are grown (results will be reported separately).
118372786
GAMMA-RAY POLARIZATION OF THE SYNCHROTRON SELF-COMPTON PROCESS FROM A HIGHLY RELATIVISTIC JET
The high polarization observed in the prompt phase of some gamma-ray bursts invites extensive study of the emission mechanism. In this paper, we investigate the polarization properties of the synchrotron self-Compton (SSC) process from a highly relativistic jet. Amagnetic-dominated, baryon-loaded jet ejected from the central engine travels with a large Lorentz factor. Shells with slightly different velocities collide with each other and produce shocks. The shocks accelerate electrons to a power-law distribution and, at the same time, magnify the magnetic field. Electrons move in the magnetic field and produce synchrotron photons. Synchrotron photons suffer from the Compton scattering (CS) process and then are detected by an observer located slightly off-axis. We analytically derive the formulae of photon polarization in the SSC process in two magnetic configurations: a magnetic field in the shock plane and perpendicular to the shock plane. We show that photons induced by the SSC process can be highly polarized, with the maximum polarization Pi similar to 24% in the energy band [0.5, 5] MeV. The polarization depends on the viewing angles, peaking in the plane perpendicular to the magnetic field. In the energy band [0.05, 0.5] MeV, in which most gamma-ray polarimeters are active, the polarization is about twice that in the Thomson limit, reaching Pi similar to 20%. This implies that the Klein-Nishina effect, which is often neglected in the literature, should be carefully considered.