1,043 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
Formal Higher Spin Gravities
We present a complete solution to the problem of Formal Higher Spin Gravities
--- formally consistent field equations that gauge a given higher spin algebra
and describe free higher spin fields upon linearization. The problem is shown
to be equivalent to constructing a certain deformation of the higher spin
algebra as an associative algebra. Given this deformation, all interaction
vertices are explicitly constructed. All formal solutions of the equations are
explicitly described in terms of an auxiliary Lax pair, the deformation
parameter playing the role of the spectral one. We also discuss a natural set
of observables associated to such theories, including the holographic
correlation functions. As an application, we give another form of the Type-B
formal Higher Spin Gravity and discuss a number of systems in five dimensions.Comment: 30 pages; typos fixed, ref adde
Slightly broken higher spin symmetry: general structure of correlators
We explore a class of CFT’s with higher spin currents and charges. Away from the free or N = ∞ limit the non-conservation of currents is governed by operators built out of the currents themselves, which deforms the algebra of charges by, and together with, its action on the currents. This structure is encoded in a certain A∞/L∞-algebra. Under quite general assumptions we construct invariants of the deformed higher spin symmetry, which are candidate correlation functions. In particular, we show that there is a finite number of independent structures at the n-point level. The invariants are found to have a form reminiscent of a one-loop exact theory. In the case of Chern-Simons vector models the uniqueness of the invariants implies the three-dimensional bosonization duality in the large-N limit
Going Off-Piste: The Role of Status in Launching Unsponsored R&D Projects
Many established organizations rely on unsponsored R&D projects to sustain and support corporate renewal. These ideas that emerge from dark corners of the organization are often the result of inventors’ proactive creative efforts. Yet, little is known about the origins of these creative efforts, and what drives individuals to decide for or against engagement in such behavior. Building on the notion of middle-status conformity, we argue for the existence of a curvilinear (U-shaped) relationship between inventors’ status and their participation in autonomous inventive efforts. We argue that this effect is further moderated by factors influencing the salience of existing status-granting institutions, specifically the novelty of the technological domain of the invention, the competitive position of the wider organization, and the inventors’ geographic location. Using a unique dataset of invention disclosures from a global technology-based firm, we find general support for our hypotheses. We propose implications for theories of innovation, networks, and status that add to our understanding of proactive forms of creative effort
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