568 research outputs found
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
Correlations of the local density of states in quasi-one-dimensional wires
We report a calculation of the correlation function of the local density of
states in a disordered quasi-one-dimensional wire in the unitary symmetry class
at a small energy difference. Using an expression from the supersymmetric
sigma-model, we obtain the full dependence of the two-point correlation
function on the distance between the points. In the limit of zero energy
difference, our calculation reproduces the statistics of a single localized
wave function. At logarithmically large distances of the order of the Mott
scale, we obtain a reentrant behavior similar to that in strictly
one-dimensional chains.Comment: Published version. Minor technical and notational improvements. 16
pages, 1 figur
Hybridization of wave functions in one-dimensional localization
A quantum particle can be localized in a disordered potential, the effect
known as Anderson localization. In such a system, correlations of wave
functions at very close energies may be described, due to Mott, in terms of a
hybridization of localized states. We revisit this hybridization description
and show that it may be used to obtain quantitatively exact expressions for
some asymptotic features of correlation functions, if the tails of the wave
functions and the hybridization matrix elements are assumed to have log-normal
distributions typical for localization effects. Specifically, we consider three
types of one-dimensional systems: a strictly one-dimensional wire and two
quasi-one-dimensional wires with unitary and orthogonal symmetries. In each of
these models, we consider two types of correlation functions: the correlations
of the density of states at close energies and the dynamic response function at
low frequencies. For each of those correlation functions, within our method, we
calculate three asymptotic features: the behavior at the logarithmically large
"Mott length scale", the low-frequency limit at length scale between the
localization length and the Mott length scale, and the leading correction in
frequency to this limit. In the several cases, where exact results are
available, our method reproduces them within the precision of the orders in
frequency considered.Comment: 10 pages, 5 figures. Several references added, minor corrections
corresponding to the journal versio
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
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