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The coupling between acoustic vibrations in a lithium niobate bulk acoustic wave resonator and microwave photons of a re-entrant microwave cavity was investigated at a temperature close to 4 K. Coupling was achieved by placing the acoustic resonator in the location of the re-entrant cavity electric field maxima, in a symmetric "split-post" configuration, with a large overlap between the microwave field and the acoustic mode, allowing acoustic modulations of the microwave frequency. We show that the acoustic modes in this setup retain large inherent quality factors of greater than $10^6$. A maximum optomechanical coupling rate was determined to be $g_0$ = 0.014 mHz, four orders of magnitude larger than previous results obtained using a quartz BAW at 4 K in a similar experimental setup, but using a single post-re-entrant cavity resonator., Comment: Accepted Version

We study the off-shell structure of the two-loop effective action in $6D, {\cal N}=(1,1)$ supersymmetric gauge theories formulated in ${\cal N}=(1,0)$ harmonic superspace. The off-shell effective action involving all fields of $6D, {\cal N}=(1,1)$ supermultiplet is constructed by the harmonic superfield background field method, which ensures both manifest gauge covariance and manifest ${\cal N}=(1,0)$ supersymmetry. We analyze the off-shell divergences dependent on both gauge and hypermultiplet superfields and argue that the gauge invariance of the divergences is consistent with the non-locality in harmonics. The two-loop contributions to the effective action are given by harmonic supergraphs with the background gauge and hypermultiplet superfields. The procedure is developed to operate with the harmonic-dependent superpropagators in the two-loop supergraphs within the superfield dimensional regularization. We explicitly calculate the gauge and the hypermultiplet-mixed divergences as the coefficients of $\frac{1}{{\varepsilon}^2}$ and demonstrate that the corresponding expressions are non-local in harmonics., Comment: 1+25 pages, appendices added

We continue studying $6D, {\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. Using the superfield background field method we explore the two-loop divergencies of the effective action in the gauge multiplet sector. It is explicitly demonstrated that among four two-loop background-field dependent supergraphs contributing to the effective action, only one diverges off shell. It is also shown that the divergences are proportional to the superfield classical equations of motion and hence vanish on shell. Besides, we have analyzed a possible structure of the two-loop divergences on general gauge and hypermultiplet background., Comment: 1+14 pages; v.2: Section 5 added, exposition in Section 1 partly changed; published version

We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $\mathcal{N}=4$ SYM superfield constraints are solved in terms of on-shell $\mathcal {N}=2$ harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $\mathcal{N}=4$ supersymmetric invariants and further rewriting them in $\mathcal{N}= 2$ harmonic superspace. In particular, we present $\mathcal{N}=4$ superfield form of the leading term in the $\mathcal{N}=4$ SYM effective action which was known previously in $\mathcal{N}=2$ superspace formulation., Comment: 45 pages, typos corrected, references, footnote and acknowledgement added

Due to their high force sensitivity, mechanical resonators combining low mechanical dissipation with a small motional mass are highly demanded in fields as diverse as resonant force imaging, mass sensing, or cavity optomechanics. "Soft-clamping" is a phononic engineering technique by which mechanical modes of highly-stressed membranes or strings are localized away from lossy regions, thereby enabling ultrahigh-Q for ng-scale devices. Here, we report on parasitic modes arising from the finite size of the structure which can significantly degrade the performance of these membranes. Through interferometric measurements and finite-element simulations, we show that these parasitic modes can hybridize with the localized modes of our structures, reducing the quality factors by up to one order of magnitude. To circumvent this problem, we engineer the spectral profile of the parasitic modes in order to avoid their overlap with the high-Q defect mode. We verify via a statistical analysis that this modal engineering reproducibly yields higher quality factors in fabricated devices, consistent with theoretically predicted values., Comment: 6 pages, 4 figures

We consider the harmonic superspace formulation of higher-derivative $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory and its minimal coupling to a hypermultiplet. In components, the kinetic term for the gauge field in such a theory involves four space-time derivatives.The theory is quantized in the framework of the superfield background method ensuring manifest $6D$, ${\cal N}=(1,0)$ supersymmetry and the classical gauge invariance of the quantum effective action. We evaluate the superficial degree of divergence and prove it to be independent of the number of loops. Using the regularization by dimensional reduction, we find possible counterterms and show that they can be removed by the coupling constant renormalization for any number of loops, while the divergences in the hypermultiplet sector are absent at all. Assuming that the deviation of the gauge-fixing term from that in the Feynman gauge is small, we explicitly calculate the divergent part of the one-loop effective action in the lowest order in this deviation. In the approximation considered, the result is independent of the gauge-fixing parameter and agrees with the earlier calculation for the theory without a hypermultiplet., Comment: Published version, 16 pages

We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of $6D$, ${\cal N}=(1,0)$ supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and ${\cal N}=(1,0)$ supersymmetric way. We exploit the regularization by dimensional reduction in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant $\beta$-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed {\it a priori}. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations., Comment: 18 pages, 1 figure, final version accepted for publication in JHEP

Using the superfield gauging procedure, we construct new ${\cal N}\,{=}\,2$ and ${\cal N}\,{=}\,4$ superfield systems that generalize Calogero models. In the bosonic limit, these systems yield rational Calogero models and hyperbolic Calogero-Sutherland models in the ${\cal N}\,{=}\,2$ case, and their ${\rm U}(2)$ spin generalization in the ${\cal N}\,{=}\,4$ case., Comment: 8 pages, Talk given by E. Ivanov at International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics". September 9-13, 2019; Moscow-Dubna, Russia

We present the explicit superfield realizations of the hidden $SU(4)$ and $O(5)$ $R$-symmetries in $4D, {\cal N}=4$ and $5D, {\cal N}=2$ supersymmetric Yang-Mills theories in the harmonic superspace approach. The $R$-symmetry transformations are constructed and their algebraic structure is studied. It is shown that such transformations are consistent with both manifest and hidden supersymmetry transformations. These symmetries can serve as an alternative tool for constructing the relevant complete low-energy superfield effective actions determined earlier from the hidden supersymmetry considerations., Comment: 0 + 27 pages, new subsection 2.1 and further clarifying comments added, typos corrected; published version

We consider $5D$, ${\cal N}=2$ supersymmetric Yang-Mills (SYM) theory in $5D$, ${\cal N}=1$ harmonic superspace as a theory of the interacting adjoint $5D$, ${\cal N}=1$ gauge multiplet and hypermultiplet. Using the background superfield method, we compute the leading low-energy contribution to the one-loop effective action. The result of quantum calculations precisely matches the effective action derived earlier in {\tt arXiv:1812.07206} on the pure symmetry grounds., Comment: 1+10 pages

For $6D$, ${\cal N}=(1,1)$ SYM theory formulated in ${\cal N}=(1,0)$ harmonic superspace as a theory of interacting gauge multiplet and hypermultiplet we construct the ${\cal N}=(1,1)$ supersymmetric Heisenberg-Euler-type superfield effective action. The effective action is computed for the slowly varying on-shell background fields and involves, in the bosonic sector, all powers of a constant abelian strength., Comment: 1+17 pages; v2: minor corrections, references added

In this review paper, we outline and exemplify the general method of constructing the supefield low-energy quantum effective action of supersymmetric Yang-Mills (SYM) theories with extended supersymmetry in the Coulomb phase, grounded upon the requirement of invariance under the non-manifest (hidden) part of the underlying supersymmetry. In this way we restore the ${\cal N}=4$ supersymmetric effective actions in $4D, {\cal N}=4$ SYM, ${\cal N}=2$ supersymmetric effective actions in $5D, {\cal N}=2$ SYM and ${\cal N}=(1,1)$ supersymmetric effective actions in $6D, {\cal N}=(1,1)$ SYM theories. The manifest off-shell fractions of the full supersymmetry are, respectively, $4D, {\cal N}=2$, $5D, {\cal N}=1$ and $6D, {\cal N}=(1,0)$ supersymmetries. In all cases the effective actions depend on the corresponding covariant superfield SYM strengths and the hypermultiplet superfields. The whole construction essentially exploits a power of the harmonic superspace formalism., Comment: 0 + 27 pages, Abstract and sec. 2 slightly modified, typos corrected; Contribution to the Volume in Honor of Andrei A. Slavnov on the occasion of his 80th Birthday. arXiv admin note: text overlap with arXiv:1812.07206, arXiv:hep-th/0111062

We study the gauge dependence of one-loop divergences in a general matter-coupled $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory in the harmonic superspace formulation. Our analysis is based on the effective action constructed by the background superfield method, with the gauge-fixing term involving one real parameter $\xi_0$. A manifestly gauge invariant and ${\cal N}=(1,0)$ supersymmetric procedure for calculating the one-loop effective action is developed. It yields the one-loop divergences in an explicit form and allows one to investigate their gauge dependence. As compared to the minimal gauge, $\xi_0=1$, the divergent part of the general-gauge effective action contains a new term depending on $\xi_0\,$. This term vanishes for the background superfields satisfying the classical equations of motion, so that the $S$-matrix divergences are gauge-independent. In the case of $6D$, ${\cal N} = (1,1)$ SYM theory we demonstrate that some divergent contributions in the non-minimal gauges do not vanish off shell, as opposed to the minimal gauge., Comment: 13 pages

We construct manifestly ${\cal N}=4$ supersymmetric off-shell superfield actions for the HKT $d=1$ sigma models on the group manifolds U(2) and SU(3), using the harmonic $d=1$ approach. The underlying $({\bf 4, 4, 0})$ and $({\bf 4, 4, 0})\oplus({\bf 4, 4, 0})$ multiplets are described, respectively, by one and two harmonic analytic superfields $q^+$ satisfying the appropriate nonlinear harmonic constraints. The invariant actions in both cases are bilinear in the superfields. We present the corresponding superfield realizations of the U(2) and SU(3) isometries and show that in fact they are enlarged to the products U(2)$\times$SU(2) and SU(3)$\times$U(2). We prove the corresponding invariances at both the superfield and component levels and present the bosonic $d=1$ sigma model actions, as integral over $t$ in the U(2) case and over $t$ and ${\rm SU}(2)$ harmonics in the SU(3) case. In the U(2) case we also give a detailed comparison with the general harmonic approach to HKT models and establish a correspondence with a particular action of the off-shell nonlinear multiplet $({\bf 3, 4, 1})$. A possible way of generalizing U(2) model to the matrix U($2n$) case is suggested., Comment: 0 + 32 pages, some typos corrected in Abstract, eqs. (2.13), (4.19) and (4.36)

Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example, to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x,p] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as amplitude-frequency effect. By implementing this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave resonator. Our experiments with sapphire resonator have established the upper limit on quantum gravity correction constant for $\beta_0<5 \times10^6$ which is a factor of 6 better than previously detected. The reasonable estimates of $\beta_0$ from experiments with quartz resonators yield an even more stringent limit of $4\times10^4$. The data sets of 1936 measurement of physical pendulum period by Atkinson results in significantly stronger limitations on $\beta_0 \ll 1$. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments, the exact upper bound on $\beta_0$ can not be reliably established. Moreover, pendulum based systems only allow testing a specific form of the modified commutator that depends on the mean value of momentum. The electro-mechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to much higher stability and a higher degree of control., Comment: 3 figures

We construct ${\cal N}=2$ supersymmetric low-energy effective action of $5D, {\cal N}=2$ supersymmetric Yang-Mills theory in $5D, {\cal N}=1$ harmonic superspace. It is obtained as a hypermultiplet completion of the leading $W \ln W$-term in the ${\cal N}=1$ SYM low-energy effective action by invoking the second implicit on-shell ${\cal N}=1$ supersymmetry. After passing to components, the ${\cal N}=2$ effective action constructed displays, along with other terms, the $SO(5)$-invariant $F^4/X^3$ term. Though we specialize to the case of $SU(2)$ gauge group spontaneously broken to $U(1)$, our consideration is applicable to any gauge symmetry broken to some abelian subgroup., Comment: 12 pages; v2: minor changes, references added

We review the recent progress in studying the quantum structure of $6D$, ${\cal N}=(1,0)$ and ${\cal N}=(1,1)$ supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly ${\cal N}=(1,0)$ supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The ${\cal N}=(1,1)$ supersymmetric Yang--Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Also some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Also in the abelian case we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action., Comment: 36 pages, 10 figures, minor corrections, some references added

We demonstrate theoretically, and confirm experimentally, that nonlinear spin waves excited in thin yttrium iron garnet films are good candidates for squeezing vacuum quantum noise. The experimental demonstration is in the form of a measurement of spin-wave induced modulation instability (IMI) conducted in the classical regime. The experiment evidences strong phase locking of an idler wave parametrically generated in the film with a deterministic small-signal wave launched into the film from an external source. The theory predicts that the same behaviour will be observed for vacuum quantum noise, resulting in squeezing of the noise.

We study the gauge dependence of the one-loop effective action for the abelian $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory formulated in harmonic superspace. We introduce the superfield $\xi$-gauge, construct the corresponding gauge superfield propagator, and calculate the one-loop two-and three-point Green functions with two external hypermultiplet legs. We demonstrate that in the general $\xi$-gauge the two-point Green function of the hypermultiplet is divergent, as opposed to the Feynman gauge $\xi =1$. The three-point Green function with two external hypermultiplet legs and one leg of the gauge superfield is also divergent. We verified that the Green functions considered satisfy the Ward identity formulated in ${\cal N}=(1,0)$ harmonic superspace and that their gauge dependence vanishes on shell. Using the result for the two- and three-point Green functions and arguments based on the gauge invariance, we present the complete divergent part of the one-loop effective action in the general $\xi$-gauge., Comment: 23 pages, 5 figures, minor corrections

The first 48-antenna stage of the Siberian Radioheliograph (SRH) started single-frequency test observations early in 2016, and since August 2016 it routinely observes the Sun at several frequencies in the 4-8 GHz range with an angular resolution of 1-2 arc minutes and an imaging interval of about 12 seconds. With limited opportunities of the incomplete antenna configuration, a high sensitivity of about 100 Jy allows the SRH to contribute to the studies of eruptive phenomena along three lines. First, some eruptions are directly visible in SRH images. Second, some small eruptions are detectable even without a detailed imaging information from microwave depressions caused by screening the background emission by cool erupted plasma. Third, SRH observations reveal new aspects of some events to be studied with different instruments. We focus on an eruptive C2.2 flare on 16 March 2016 around 06:40, one of the first flares observed by the SRH. Proceeding from SRH observations, we analyze this event using extreme-ultraviolet, hard X-ray, white-light, and metric radio data. An eruptive prominence expanded, brightened, and twisted, which indicates a time-extended process of the flux-rope formation together with the development of a large coronal mass ejection (CME). The observations rule out a passive role of the prominence in the CME formation. The abrupt prominence eruption impulsively excited a blast-wave-like shock, which appeared during the microwave burst and was manifested in an "EUV wave" and Type II radio burst. The shock wave decayed and did not transform into a bow shock because of the low speed of the CME. Nevertheless, this event produced a clear proton enhancement near Earth. Comparison with our previous studies of several events confirms that the impulsive-piston shock-excitation scenario is typical of various events., Comment: 25 pages, 21 figures, 1 table. Published in Journal of Atmospheric and Solar-Terrestrial Physics. For associated movie files, see http://iszf.irk.ru/~grechnev/papers/SRH_eruptions/

We explain how a generic HKT geometry can be derived using the language of N = 4 supersymmetric quantum mechanics. To this end, one should consider a Lagrangian involving several (4,4,0) multiplets defined in harmonic superspace and subject to nontrivial harmonic constraints. Conjecturally, this general construction worked out earlier by Delduc and Ivanov gives a complete classification of all HKT geometries. Each such geometry is generated by two different functions (potentials) of a special type that depend on harmonic superfields and on harmonics. Given these two potentials, one can derive the vielbeins, metric, connections and curvatures, but this is not so simple: one should solve rather complicated differential equations. We illustrate the general construction by giving a detailed derivation of the metric for the hyper-Kaehler Taub-NUT manifold. In the generic case, we arrive at an HKT geometry. In this paper, we give a simple proof of this assertion., Comment: 43 pages

We consider $6D$, ${\cal N}=(1,1)$ supersymmetric Yang-Mills theory formulated in ${\cal N}=(1,0)$ harmonic superspace and analyze the structure of the two-loop divergences in the hypermultiplet sector. Using the ${\cal N}=(1,0)$ superfield background field method we study the two-point supergraphs with the hypermultiplet legs and prove that their total contribution to the divergent part of effective action vanishes off shell., Comment: 8 pages, 2 figures

We elaborate on the low-energy effective action of $6D,\,{\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. The theory is described in terms of analytic ${\cal N}=(1,0)$ gauge superfield $V^{++}$ and analytic $\omega$-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest ${\cal N}=(1,0)$ supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group $SU(N)$ is broken to $SU(N-1)\times U(1)\subset SU(N)$. In the bosonic sector the effective action involves the structure $\sim \frac{F^4}{X^2}$, where $F^4$ is a monomial of the fourth degree in an abelian field strength $F_{MN}$ and $X$ stands for the scalar fields from the $\omega$-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff., Comment: 1+14 pages, text essentially remade, some references added, title is slightly corrected

Regular observations of active processes in the solar atmosphere have been started using the first stage of the multiwave Siberian Radioheliograph (SRH), a T-shaped 48-antenna array with a 4-8 GHz operating frequency range and a 10 MHz instantaneous receiving band. Antennas are mounted on the central antenna posts of the Siberian Solar Radio Telescope. The maximum baseline is 107.4 m, and the angular resolution is up to 70". We present examples of observations of the solar disk at different frequencies, "negative" bursts, and solar flares. The sensitivity to compact sources reaches 0.01 solar flux units ($\approx 10^{-4}$ of the total solar flux) with an accumulation time of about 0.3 s. The high sensitivity of SRH enables monitoring of solar activity and allows studying active processes from characteristics of their microwave emission, including faint events, which could not be detected previously., Comment: 14 pages, 12 figures