6,975 research outputs found
On Christoffel and standard words and their derivatives
We introduce and study natural derivatives for Christoffel and finite
standard words, as well as for characteristic Sturmian words. These
derivatives, which are realized as inverse images under suitable morphisms,
preserve the aforementioned classes of words. In the case of Christoffel words,
the morphisms involved map to (resp.,~) and to
(resp.,~) for a suitable . As long as derivatives are
longer than one letter, higher-order derivatives are naturally obtained. We
define the depth of a Christoffel or standard word as the smallest order for
which the derivative is a single letter. We give several combinatorial and
arithmetic descriptions of the depth, and (tight) lower and upper bounds for
it.Comment: 28 pages. Final version, to appear in TC
Frame-like Geometry of Double Field Theory
We relate two formulations of the recently constructed double field theory to
a frame-like geometrical formalism developed by Siegel. A self-contained
presentation of this formalism is given, including a discussion of the
constraints and its solutions, and of the resulting Riemann tensor, Ricci
tensor and curvature scalar. This curvature scalar can be used to define an
action, and it is shown that this action is equivalent to that of double field
theory.Comment: 35 pages, v2: minor corrections, to appear in J. Phys.
E Exceptional Field Theory: Geometry, Fermions and Supersymmetry
We present the supersymmetric extension of the recently constructed
E exceptional field theory -- the manifestly U-duality covariant
formulation of the untruncated ten- and eleven-dimensional supergravities. This
theory is formulated on a (3+248) dimensional spacetime (modulo section
constraint) in which the extended coordinates transform in the adjoint
representation of E. All bosonic fields are E tensors and
transform under internal generalized diffeomorphisms. The fermions are tensors
under the generalized Lorentz group SO(1,2)SO(16), where SO(16) is the
maximal compact subgroup of E. Vanishing generalized torsion
determines the corresponding spin connections to the extent they are required
to formulate the field equations and supersymmetry transformation laws. We
determine the supersymmetry transformations for all bosonic and fermionic
fields such that they consistently close into generalized diffeomorphisms. In
particular, the covariantly constrained gauge vectors of E exceptional
field theory combine with the standard supergravity fields into a single
supermultiplet. We give the complete extended Lagrangian and show its
invariance under supersymmetry. Upon solution of the section constraint the
theory reduces to full D=11 or type IIB supergravity.Comment: 25 page
Finite W_3 Transformations in a Multi-time Approach
Classical {\W} transformations are discussed as restricted diffeomorphism
transformations (\W-Diff) in two-dimensional space. We formulate them by using
Riemannian geometry as a basic ingredient. The extended {\W} generators are
given as particular combinations of Christoffel symbols. The defining equations
of \W-Diff are shown to depend on these generators explicitly. We also consider
the issues of finite transformations, global transformations and
\W-Schwarzians.Comment: 10 pages, UB-ECM-PF 94/20, TOHO-FP-9448, QMW-PH-94-2
Geometry and dynamics of higher-spin frame fields
We give a systematic account of unconstrained free bosonic higher-spin fields
on D-dimensional Minkowski and (Anti-)de Sitter spaces in the frame formalism.
The generalized spin connections are determined by solving a chain of
torsion-like constraints. Via a generalization of the vielbein postulate these
allow to determine higher-spin Christoffel symbols, whose relation to the de
Wit--Freedman connections is discussed. We prove that the generalized Einstein
equations, despite being of higher-derivative order, give rise to the AdS
Fronsdal equations in the compensator formulation. To this end we derive
Damour-Deser identities for arbitrary spin on AdS. Finally we discuss the
possibility of a geometrical and local action principle, which is manifestly
invariant under unconstrained higher-spin symmetries.Comment: 30 pages, uses youngtab.sty, v2: minor changes, references adde
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