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 $sp(2n)$ symmetry from the corresponding cycles. A particular case of $sp(4)$ may be relevant for the on-shell action of the $4d$ 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

Energy relaxation rate and its mesoscopic fluctuations in quantum dots

We analyze the applicability of the Fermi-golden-rule description of quasiparticle relaxation in a closed diffusive quantum dot with electron-electron interaction. Assuming that single-particle levels are already resolved but the initial stage of quasiparticle disintegration can still be described by a simple exponential decay, we calculate the average inelastic energy relaxation rate of single-particle excitations and its mesoscopic fluctuations. The smallness of mesoscopic fluctuations can then be used as a criterion for the validity of the Fermi-golden-rule description. Technically, we implement the real-space Keldysh diagram technique, handling correlations in the quasi-discrete spectrum non-perturbatively by means of the non-linear supersymmetric sigma model. The unitary symmetry class is considered for simplicity. Our approach is complementary to the lattice-model analysis of Fock space: thought we are not able to describe many-body localization, we derive the exact lowest-order expression for mesoscopic fluctuations of the relaxation rate, making no assumptions on the matrix elements of the interaction. It is shown that for the quasiparticle with the energy $\varepsilon$ on top of the thermal state with the temperature $T$, fluctuations of its energy width become large and the Fermi-golden-rule description breaks down at $\max\{\varepsilon,T\}\sim\Delta\sqrt{g}$, where $\Delta$ is the mean level spacing in the quantum dot, and $g$ is its dimensionless conductance.Comment: 33 pages, 9 figure

Superconducting fluctuations at arbitrary disorder strength

We study the effect of superconducting fluctuations on the conductivity of metals at arbitrary temperatures $T$ and impurity scattering rates $\tau^{-1}$. Using the standard diagrammatic technique but in the Keldysh representation, we derive the general expression for the fluctuation correction to the dc conductivity applicable for any space dimensionality and analyze it the case of the film geometry. We observe that the usual classification in terms of the Aslamazov-Larkin, Maki-Thompson and density-of-states diagrams is to some extent artificial since these contributions produce similar terms, which partially cancel each other. In the diffusive limit, our results fully coincide with recent calculations in the Keldysh technique. In the ballistic limit near the transition, we demonstrate the absence of a divergent term $(T\tau)^2$ attributed previously to the density-of-states contribution. In the ballistic limit far above the transition, the temperature-dependent part of the conductivity correction is shown to scale roughly as $T\tau$.Comment: 17 pages, 7 figures. A figure illustrating the temperature dependence of the fluctuation correction is added; the sign of the high-temperature asymptote in the ballistic case is fixe

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