354 research outputs found
Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex
In the eighties, Berends, Burgers and van Dam (BBvD) found a nonabelian cubic
vertex for self-interacting massless fields of spin three in flat spacetime.
However, they also found that this deformation is inconsistent at higher order
for any multiplet of spin-three fields. For arbitrary symmetric gauge fields,
we severely constrain the possible nonabelian deformations of the gauge algebra
and, using these results, prove that the BBvD obstruction cannot be cured by
any means, even by introducing fields of spin higher (or lower) than three.Comment: 19 pages, no figur
An action principle for Vasiliev's four-dimensional higher-spin gravity
We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge
fields in four spacetime dimensions with an action principle. We first extend
Vasiliev's original system with differential forms in degrees higher than one.
We then derive the resulting duality-extended equations of motion from a
variational principle based on a generalized Hamiltonian sigma-model action.
The generalized Hamiltonian contains two types of interaction freedoms: One set
of functions that appears in the Q-structure of the generalized curvatures of
the odd forms in the duality-extended system; and another set depending on the
Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of
polyvector fields of ranks two or higher in target space. We find that at least
one of the two sets of interaction-freedom functions must be linear in order to
ensure gauge invariance. We discuss consistent truncations to the minimal Type
A and B models (with only even spins), spectral flows on-shell and provide
boundary conditions on fields and gauge parameters that are compatible with the
variational principle and that make the duality-extended system equivalent, on
shell, to Vasiliev's original system.Comment: 37 pages. References added, corrected typo
Supersymmetric Higher Spin Theories
We revisit the higher spin extensions of the anti de Sitter algebra in four
dimensions that incorporate internal symmetries and admit representations that
contain fermions, classified long ago by Konstein and Vasiliev. We construct
the , Euclidean and Kleinian version of these algebras, as well as the
corresponding fully nonlinear Vasiliev type higher spin theories, in which the
reality conditions we impose on the master fields play a crucial role. The
supersymmetric higher spin theory in , on which we elaborate
further, is included in this class of models. A subset of Konstein-Vasiliev
algebras are the higher spin extensions of the superalgebras
for mod 4 and can be realized using
fermionic oscillators. We tensor the higher superalgebras of the latter kind
with appropriate internal symmetry groups and show that the mod 4
higher spin algebras are isomorphic to those with mod 4. We
describe the fully nonlinear higher spin theories based on these algebras as
well, and we elaborate further on the supersymmetric theory,
providing two equivalent descriptions one of which exhibits manifestly its
relation to the supersymmetric higher spin theory.Comment: 30 pages. Contribution to J. Phys. A special volume on "Higher Spin
Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie
The minimal conformal O(N) vector sigma model at d=3
For the minimal O(N) sigma model, which is defined to be generated by the
O(N) scalar auxiliary field alone, all n-point functions, till order 1/N
included, can be expressed by elementary functions without logarithms.
Consequently, the conformal composite fields of m auxiliary fields possess at
the same order such dimensions, which are m times the dimension of the
auxiliary field plus the order of differentiation.Comment: 15 page
On gravitational interactions for massive higher spins in
In this paper we investigate gravitational interactions of massive higher
spin fields in three dimensional space with arbitrary value of
cosmological constant including flat Minkowski space. We use frame-like gauge
description for such massive fields adopted to three-dimensional case. At
first, we carefully analyze the procedure of switching on gravitational
interactions in the linear approximation on the example of massive spin-3 field
and then proceed with the generalization to the case of arbitrary integer spin
field. As a result we construct a cubic interaction vertex linear in spin-2
field and quadratic in higher spin field on background. As in the
massless case the vertex does not contain any higher derivative corrections to
the Lagrangian and/or gauge transformations. Thus, even after switching on
gravitational interactions, one can freely consider any massless or partially
massless limits as well as the flat one.Comment: 21 pages. Some clarifications and 1 new reference added. Version to
appear in the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT"
edited by Matthias Gaberdiel and Mikhail Vasilie
A minimal BV action for Vasiliev's four-dimensional higher spin gravity
The action principle for Vasiliev's four-dimensional higher-spin gravity
proposed recently by two of the authors, is converted into a minimal BV master
action using the AKSZ procedure, which amounts to replacing the classical
differential forms by vectorial superfields of fixed total degree given by the
sum of form degree and ghost number. The nilpotency of the BRST operator is
achieved by imposing boundary conditions and choosing appropriate gauge
transitions between charts leading to a globally-defined formulation based on a
principal bundle.Comment: 39 pages, 1 figure. Additional comments in the conclusion
Gauge fields and infinite chains of dualities
We show that the particle states of Maxwell's theory, in dimensions, can
be represented in an infinite number of ways by using different gauge fields.
Using this result we formulate the dynamics in terms of an infinite set of
duality relations which are first order in space-time derivatives. We derive a
similar result for the three form in eleven dimensions where such a possibility
was first observed in the context of E11. We also give an action formulation
for some of the gauge fields. In this paper we give a pedagogical account of
the Lorentz and gauge covariant formulation of the irreducible representations
of the Poincar\'e group, used previously in higher spin theories, as this plays
a key role in our constructions. It is clear that our results can be
generalised to any particle.Comment: 37 page
Invariant Differential Operators and Characters of the AdS_4 Algebra
The aim of this paper is to apply systematically to AdS_4 some modern tools
in the representation theory of Lie algebras which are easily generalised to
the supersymmetric and quantum group settings and necessary for applications to
string theory and integrable models. Here we introduce the necessary
representations of the AdS_4 algebra and group. We give explicitly all singular
(null) vectors of the reducible AdS_4 Verma modules. These are used to obtain
the AdS_4 invariant differential operators. Using this we display a new
structure - a diagram involving four partially equivalent reducible
representations one of which contains all finite-dimensional irreps of the
AdS_4 algebra. We study in more detail the cases involving UIRs, in particular,
the Di and the Rac singletons, and the massless UIRs. In the massless case we
discover the structure of sets of 2s_0-1 conserved currents for each spin s_0
UIR, s_0=1,3/2,... All massless cases are contained in a one-parameter
subfamily of the quartet diagrams mentioned above, the parameter being the spin
s_0. Further we give the classification of the so(5,C) irreps presented in a
diagramatic way which makes easy the derivation of all character formulae. The
paper concludes with a speculation on the possible applications of the
character formulae to integrable models.Comment: 30 pages, 4 figures, TEX-harvmac with input files: amssym.def,
amssym.tex, epsf.tex; version 2 1 reference added; v3: minor corrections;
v.4: minor corrections, v.5: minor corrections to conform with version in J.
Phys. A: Math. Gen; v.6.: small correction and addition in subsections 4.1 &
4.
Deformation independent open brane metrics and generalized theta parameters
We investigate the consequences of generalizing certain well established
properties of the open string metric to the conjectured open membrane and open
Dp-brane metrics. By imposing deformation independence on these metrics their
functional dependence on the background fields can be determined including the
notorious conformal factor. In analogy with the non-commutativity parameter
in the string case, we also obtain `generalized' theta
parameters which are rank q+1 antisymmetric tensors (polyvectors) for open
Dq-branes and rank 3 for the open membrane case. The expressions we obtain for
the open membrane quantities are expected to be valid for general background
field configurations, while the open D-brane quantities are only valid for one
parameter deformations. By reducing the open membrane data to five dimensions,
we show that they, modulo a subtlety with implications for the relation between
OM-theory and NCYM, correctly generate the open string and open D2-data.Comment: 24 pages, LaTe
Iron Age and Anglo-Saxon genomes from East England reveal British migration history
British population history has been shaped by a series of immigrations, including the early Anglo-Saxon migrations after 400 CE. It remains an open question how these events affected the genetic composition of the current British population. Here, we present whole-genome sequences from 10 individuals excavated close to Cambridge in the East of England, ranging from the late Iron Age to the middle Anglo-Saxon period. By analysing shared rare variants with hundreds of modern samples from Britain and Europe, we estimate that on average the contemporary East English population derives 38% of its ancestry from Anglo-Saxon migrations. We gain further insight with a new method, rarecoal, which infers population history and identifies fine-scale genetic ancestry from rare variants. Using rarecoal we find that the Anglo-Saxon samples are closely related to modern Dutch and Danish populations, while the Iron Age samples share ancestors with multiple Northern European populations including Britain
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