scholarly journals AdS3/AdS2 degression of massless particles

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Konstantin Alkalaev ◽  
Alexander Yan
Keyword(s):  
Massless Particle ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Spin Representation ◽  
Theoretical Terms ◽  
Finite Spectrum ◽  
Branching Rules ◽  
Higher Spin ◽  
Massless Fields ◽  
Kaluza Klein

Abstract We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS3 space foliated into AdS2 hypersurfaces. It is shown that an AdS3 massless particle of spin s = 1, 2, …, ∞ degresses into a couple of AdS2 particles of equal energies E = s. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS3/AdS2 degression we consider branching rules for AdS3 isometry algebra o(2,2) representations decomposed with respect to AdS2 isometry algebra o(1,2). We find that a given o(2,2) higher-spin representation lying on the unitary bound (i.e. massless) decomposes into two equal o(1,2) modules. In the field-theoretical terms, this phenomenon is demonstrated for spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can be seen by using particular mode expansions, (partial) diagonalizations, and identities specific to two dimensions.

scholarly journals Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems with Rough Data

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Konrad Simon ◽  
Jörn Behrens
Keyword(s):  
Nonlinear Problems ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Multiscale Methods ◽  
Galerkin Methods ◽  
Standard Methods ◽  
Multiscale Problems ◽  
Eulerian Method ◽  
Lower Order Terms ◽  
New Framework

AbstractWe introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when the model involves dominant lower order terms. Our idea to overcome the associated difficulties is a semi-Lagrangian based reconstruction of subgrid variability into a multiscale basis by solving many local inverse problems. Globally the method looks like a Eulerian method with multiscale stabilized basis. We show example runs in one and two dimensions and a comparison to standard methods to support our ideas and discuss possible extensions to other types of Galerkin methods, higher dimensions and nonlinear problems.

scholarly journals Matter-free higher spin gravities in 3D: Partially-massless fields and general structure

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
Maxim Grigoriev ◽  
Karapet Mkrtchyan ◽  
Evgeny Skvortsov
Keyword(s):  
General Structure ◽  
Higher Spin ◽  
Massless Fields

scholarly journals Two-Column Higher-Spin Massless Fields in AdSdSpace

2004 ◽  
Vol 140 (3) ◽  
pp. 1253-1263 ◽  
Author(s):  
K. B. Alkalaev
Keyword(s):  
Higher Spin ◽  
Massless Fields

scholarly journals NEW DISCRETE STATES IN TWO-DIMENSIONAL SUPERGRAVITY

2007 ◽  
Vol 22 (07) ◽  
pp. 1375-1394 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Operator Algebra ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Field Theories ◽  
Two Dimensional ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving ◽  
Volume Preserving ◽  
Lowering Operator

Two-dimensional string theory is known to contain the set of discrete states that are the SU (2) multiplets generated by the lowering operator of the SU (2) current algebra. Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. In this paper we show that the interaction of d = 2 superstrings with the superconformal β - γ ghosts enlarges the actual algebra of the dimension 1 currents and hence the new ghost-dependent discrete states appear. Generally, these states are the SU (N) multiplets if the algebra includes the currents of ghost numbers n : -N ≤ n ≤ N - 2, not related by picture changing. We compute the structure constants of these ghost-dependent discrete states for N = 3 and express them in terms of SU (3) Clebsch–Gordan coefficients, relating this operator algebra to the volume preserving diffeomorphisms in d = 3. For general N, the operator algebra is conjectured to be isomorphic to SDiff (N). This points at possible holographic relations between two-dimensional superstrings and field theories in higher dimensions.

Critical intensities of Boolean models with different underlying convex shapes

2002 ◽  
Vol 34 (01) ◽  
pp. 48-57
Author(s):  
Rahul Roy ◽  
Hideki Tanemura
Keyword(s):  
Unit Area ◽  
Higher Dimensions ◽  
Boolean Model ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Boolean Models ◽  
Regular Polytope ◽  
Minimum Value ◽  
Critical Intensity ◽  
Poisson Boolean Model

We consider the Poisson Boolean model of percolation where the percolating shapes are convex regions. By an enhancement argument we strengthen a result of Jonasson (2000) to show that the critical intensity of percolation in two dimensions is minimized among the class of convex shapes of unit area when the percolating shapes are triangles, and, for any other shape, the critical intensity is strictly larger than this minimum value. We also obtain a partial generalization to higher dimensions. In particular, for three dimensions, the critical intensity of percolation is minimized among the class of regular polytopes of unit volume when the percolating shapes are tetrahedrons. Moreover, for any other regular polytope, the critical intensity is strictly larger than this minimum value.

A GEOMETRIC FIELD THEORY OF CLOSED STRINGS: D=4, N=1 LOOP SUPERGRAVITY

1990 ◽  
Vol 05 (09) ◽  
pp. 1819-1832
Author(s):  
Leonardo Castellani
Keyword(s):  
Field Theory ◽  
Classical Field Theory ◽  
Energy Limit ◽  
Field Equations ◽  
Mass Generation ◽  
Infinite Dimensional ◽  
Internal Loop ◽  
Higher Spin ◽  
Spin Fields ◽  
Kaluza Klein

We present a classical field theory of interacting loops, whose low energy limit is D=4, N=1 supergravity. In Fourier modes, the theory is obtained by gauging the infinite dimensional algebra KM (SuperPoincaré) ⊕ Virasoro, where KM indicates the Kac-Moody extension. Taylor expanding the superloop vielbein in the “internal” coordinates yields towers of D=4 fields with arbitrarily high spins. The superloop diffeomorphisms relate all the higher spin fields. The field equations are obtained by requiring the closure of the generalized supersymmetries. Two different mechanisms give rise to masses for the higher modes: (i) a Kaluza-Klein type mass generation from “internal” loop coordinates, (ii) a non-vanishing background value for the zero mode of the Virasoro gauge field.

scholarly journals ANTI-DE SITTER GRAVITY FROM BF–CHERN–SIMONS–HIGGS THEORIES

2002 ◽  
Vol 17 (32) ◽  
pp. 2095-2103 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Isometry Group ◽  
Star Product ◽  
Constant Term ◽  
Higgs Potential ◽  
De Sitter ◽  
Potential Term ◽  
Higher Spin ◽  
Noncommutative Gravity ◽  
Chern Simons ◽  
Massless Fields

It is shown that an action inspired from a BF and Chern–Simons model, based on the AdS4 isometry group SO(3,2), with the inclusion of a Higgs potential term, furnishes the MacDowell–Mansouri–Chamseddine–West action for gravity, with a Gauss–Bonnet and cosmological constant term. The AdS4 space is a natural vacuum of the theory. Using Vasiliev's procedure to construct higher spin massless fields in AdS spaces and a suitable star product, we discuss the preliminary steps to construct the corresponding higher-spin action in AdS4 space representing the higher spin extension of this model. Brief remarks on noncommutative gravity are made.

Asymptotic properties of the equilibrium probability of identity in a geographically structured population

1977 ◽  
Vol 9 (2) ◽  
pp. 268-282 ◽  
Author(s):  
Stanley Sawyer
Keyword(s):  
Nearest Neighbor ◽  
Asymptotic Properties ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Order Zero ◽  
Structured Population ◽  
Equilibrium Probability ◽  
Migration Law

Let I(x, u) be the probability that two genes found a vector distance x apart are the same type in an infinite-allele selectively-neutral migration model with mutation rate u. The creatures involved inhabit an infinite of colonies, are diploid and are held at N per colony. Set in one dimension and in higher dimensions, where σ2 is the covariance matrix of the migration law (which is assumed to have finite fifth moments). Then in one dimension, in two dimensions, and in three dimensions uniformly for Here C0 is a constant depending on the migration law, K0(y) is the Bessel function of the second kind of order zero, and are the eigenvalues of σ2. For symmetric nearest-neighbor migrations, in one dimension and log mi in two. For is known in one dimension and C0 does not appear. In two dimensions, These results extend and make more precise earlier work of Malécot, Weiss and Kimura and Nagylaki.

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