1,284 research outputs found
Algebras from Slightly Broken Higher Spin Symmetries
We define a class of -algebras that are obtained by deformations of
higher spin symmetries. While higher spin symmetries of a free CFT form an
associative algebra, the slightly broken higher spin symmetries give rise to a
minimal -algebra extending the associative one. These
-algebras are related to non-commutative deformation quantization
much as the unbroken higher spin symmetries result from the conventional
deformation quantization. In the case of three dimensions there is an
additional parameter that the -structure depends on, which is to be
related to the Chern-Simons level. The deformations corresponding to the
bosonic and fermionic matter lead to the same -algebra, thus
manifesting the three-dimensional bosonization conjecture. In all other cases
we consider, the -deformation is determined by a generalized free
field in one dimension lower.Comment: 48 pages, some pictures; typos fixed, presentation improve
Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
The formal algebraic structures that govern higher-spin theories within the
unfolded approach turn out to be related to an extension of the Kontsevich
Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one
to construct the Hochschild cocycles of higher-spin algebras that make the
interaction vertices. As an application of these results we construct a family
of Vasiliev-like equations that generate the Hochschild cocycles with
symmetry from the corresponding cycles. A particular case of may be
relevant for the on-shell action of the theory. We also give the exact
equations that describe propagation of higher-spin fields on a background of
their own. The consistency of formal higher-spin theories turns out to have a
purely geometric interpretation: there exists a certain symplectic invariant
associated to cutting a polytope into simplices, namely, the Alexander-Spanier
cocycle.Comment: typos fixed, many comments added, 36 pages + 20 pages of Appendices,
3 figure
How an accelerator can catalyse your ecosystem
Many industries from IT to car manufacturing, robotic and biotechnology, competition is moving from the product level to the ecosystem level. The creation of an ecosystem by a rival and the consequent shift to ecosystem competition can be quite challenging for product-focused incumbent organisations who may find that they have a challenge to establish the reputation and legitimacy of their own new ecosystem. This article discusses the ways and means an incumbent organisation can adopt and mobilise their own ecosystem
Consistent interactions and involution
Starting from the concept of involution of field equations, a universal
method is proposed for constructing consistent interactions between the fields.
The method equally well applies to the Lagrangian and non-Lagrangian equations
and it is explicitly covariant. No auxiliary fields are introduced. The
equations may have (or have no) gauge symmetry and/or second class constraints
in Hamiltonian formalism, providing the theory admits a Hamiltonian
description. In every case the method identifies all the consistent
interactions.Comment: Minor misprints corrected, to appear in JHE
Classical and quantum stability of higher-derivative dynamics
We observe that a wide class of higher-derivative systems admits a bounded
integral of motion that ensures the classical stability of dynamics, while the
canonical energy is unbounded. We use the concept of a Lagrange anchor to
demonstrate that the bounded integral of motion is connected with the
time-translation invariance. A procedure is suggested for switching on
interactions in free higher-derivative systems without breaking their
stability. We also demonstrate the quantization technique that keeps the
higher-derivative dynamics stable at quantum level. The general construction is
illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative
scalar field model, and the Podolsky electrodynamics. For all these models, the
positive integrals of motion are explicitly constructed and the interactions
are included such that keep the system stable.Comment: 39 pages, minor corrections, references adde
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