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We perform a detailed analysis of the vacua of omega-deformed SO(8) supergravity in four dimensions. In particular, using Tensorflow-based numerical methods, we track how the equilibria of the theory change when varying the electric-magnetic deformation parameter omega. Apart from describing various properties of different equilibria (390 in total), we show that as w is deformed, the SO(3), N= 1 vacuum of the de Wit-Nicolai theory becomes equivalent to a critical point in U(4) proportional to R-12 gauged supergravity with a known uplift in IIB supergravity. The procedure employed here to obtain a new gauging with a guaranteed equilibrium is generic and allows one to obtain further admissible noncompact gaugings via omega-deformation, all of which have guaranteed critical points, and some of which may be novel upliftable solutions., Journal of High Energy Physics, 2022 (6), ISSN:1126-6708, ISSN:1029-8479

We identify 219 AdS$_4$ solutions in four-dimensional dyonically gauged ISO(7) $\mathcal{N}=8$ supergravity and present some of their properties. One of the new solutions preserves $\mathcal{N}=1$ supersymmetry and provides a rare explicit example of an AdS$_4$ vacuum dual to a 3d SCFT with no continuous global symmetry. There are also two new non-supersymmetric solutions for which all 70 scalar fields in the supergravity theory have masses above the BF bound. All of these AdS$_4$ solutions can be uplifted to massive type IIA supergravity. Motivated by this we present the low lying operator spectra of the dual 3d CFTs for all known supersymmetric AdS$_4$ solutions in the theory and organize them into superconformal multiplets., Comment: 27 pages. v2: Minor corrections

The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional N $$ \mathcal{N} $$ = 8, SO(8) gauged supergravity using Machine Learning software in [1] has led to a discovery of a new N $$ \mathcal{N} $$ = 1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3) × ℤ2-invariant truncation of the N $$ \mathcal{N} $$ = 8 theory to an N $$ \mathcal{N} $$ = 1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the N $$ \mathcal{N} $$ = 1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3) × ℤ2-invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional ℤ 2 3 $$ {\mathbb{Z}}_2^3 $$ -invariant scalar manifold (SU(1, 1)/U(1))7, for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new N $$ \mathcal{N} $$ = 1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an N $$ \mathcal{N} $$ = 1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.

The author suggests an attribution for two largely unknown Baroque sculptures inside the Church of St. Peter and Paul at Potsdam. The crucifixus, which has so far not been attributed to an artist, is shown to exhibit parallels to a 1716 work by Paul Egell. It remains unclear, however, whether the Potsdam crucifixus was also created by Egell himself or by Johann Peter Benckert, who congenially completed it in 1763 with a statue of the kneeling Maria Magdalena. The appealing depiction of the saint as an elegant sinner and penitent offers believers various possibilities for identification.

The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic temporal coding ability present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual neuron spikes. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. This temporal coding scheme allows the supervised training of the network with backpropagation, using locally exact derivatives of the postsynaptic spike times with respect to presynaptic spike times. The network operates using a biologically-plausible alpha synaptic transfer function. Additionally, we use trainable synchronisation pulses that provide bias, add flexibility during training and exploit the decay part of the alpha function. We show that such networks can be trained successfully on noisy Boolean logic tasks and on the MNIST dataset encoded in time. The results show that the spiking neural network outperforms comparable spiking models on MNIST and achieves similar quality to fully connected conventional networks with the same architecture. We also find that the spiking network spontaneously discovers two operating regimes, mirroring the accuracy-speed trade-off observed in human decision-making: a slow regime, where a decision is taken after all hidden neurons have spiked and the accuracy is very high, and a fast regime, where a decision is taken very fast but the accuracy is lower. These results demonstrate the computational power of spiking networks with biological characteristics that encode information in the timing of individual neurons. By studying temporal coding in spiking networks, we aim to create building blocks towards energy-efficient and more complex biologically-inspired neural architectures., Open-source code related to this paper is available at https://github.com/google/ihmehimmeli v2: Added references and added some clarifications for the methods

Maximal and non-maximal supergravities in three dimensions allow for a large variety of semisimple (Chern-Simons) gauge groups. In this paper, we analyze non-semisimple and complex gauge groups that satisfy the pertinent consistency relations for a maximal (N=16) gauged supergravity to exist. We give a general procedure how to generate non-semisimple gauge groups from known admissible semisimple gauge groups by a singular boost within E_{8(8)}. Examples include the theories with gauge group SO(8) x T_{28} that describe the reduction of IIA/IIB supergravity on the seven-sphere. In addition, we exhibit two `strange embeddings' of the complex gauge group SO(8,C) into (real) E_{8(8)} and prove that both can be consistently gauged. We discuss the structure of the associated scalar potentials as well as their relation to those of D>3 gauged supergravities., LaTeX2e, 30 pages; v2: minor corrections, version published in CMP

We analyze the scalar potentials of maximal gauged three-dimensional supergravities which reveal a surprisingly rich structure. In contrast to maximal supergravities in dimensions D>3, all these theories admit a maximally supersymmetric (N=16) ground state with negative cosmological constant Lambda3 theories., LaTeX2e, 46 pages

Five nontrivial stationary points are found for maximal gauged N=16 supergravity in three dimensions with gauge group $SO(8)\times SO(8)$ by restricting the potential to a submanifold of the space of $SU(3)\subset(SO(8)\times SO(8))_{\rm diag}$ singlets. The construction presented here uses the embedding of $E_{7(+7)}\subset E_{8(+8)}$ to lift the analysis of N=8, D=4 supergravity performed by N. Warner to N=16, D=3, and hence, these stationary points correspond to some of the known extrema of gauged N=8, D=4 supergravity., Comment: 16 pages, 1 figure

Exchange springs are formed in multilayers of alternating hard and soft ferromagnetic materials which are exchange coupled at their interfaces. These systems are rich of interesting physical properties, which can be tuned by selecting suitable geometries and compositions. In this paper, we present a computational study of the dynamics of a tri-layer DyFe2/YFe2/DyFe2 exchange spring system near the bending field (the field required to twist the magnetization of the soft YFe2 layer out of the aligned state). The dynamical reaction of the system to small variations of the applied field is studied and its oscillatory nature is analyzed numerically. The behaviors of the decay times, the frequencies, and amplitudes reveal enhanced responses of the system near the bending field.

Am Schicksal einer Bronzestatue des ersten preußischen Königs können die Konkurrenz und der Bedeutungswandel von Insignien ein Jahrhundert lang, von 1713 bis 1814, verfolgt werden. Zunächst war das Zepter in der Hand des Königs allen unerläßlich, auf königlichen Wunsch hin zierte das Haupt ein Lorbeerkranz, die Krone sank zur Sockelzierde herab. 1802 war der Lorbeerkranz verzichtbar und Bürger und Adel nahmen dem König das Zepter aus der Hand, Zepter und Krone wurden verkleinert und zur Seite des Sockels gedrängt. Schließlich wünschten Bürger und Adel wieder ein formgleiches, aber inhaltlich geändertes Zepter in Händen des Königs, das nicht mehr sie beherrschen sollte, sondern mit dem sie selbst als Nation über andere herrschten. A bronze statue of the first Prussian king exemplifies the competition between insignia and changes in their meaning. Th is development can be traced for the course of a century, from 1713 to 1814. Initially, the sceptre in the king’s hand was universally regarded as the central item; by specific decree laurel crowned his head, whereas the crown only appeared on the plinth. In 1802 the laurel was discarded, bourgeoisie and aristocracy took the sceptre from the king’s hand, sceptre and crown were reduced in size and moved to the side of the plinth. In the end, the meaning of the sceptre that had again been added, unchanged in form, was changed by bourgeoisie and aristocracy. The sceptre no longer ruled them, serving as a symbol of regal authority, but instead stood for the nation and its rule over others.

FlowPy is a numerical toolbox for the solution of partial differential equations encountered in Functional Renormalization Group equations. This toolbox compiles flow equations to fast machine code and is able to handle coupled systems of flow equations with full momentum dependence, which furthermore may be given implicitly., Comment: 19 pages, 3 figures; update fixes some bugs in the code

Some magnetic materials show a magnetoelectric coupling between inhomogeneous magnetization patterns and electric polarization that is sufficiently strong to allow external control of magnetization structure by electric fields. Numerical simulations of “magnetoelectric” materials of this type require an extension of the standard micromagnetic model which conceptually parallels the introduction of spin-current interaction terms. We show how the micromagnetic simulator “Nmag” can be extended to support the inhomogeneous magnetoelectric interaction term and also give a simple self-contained example for simulating the micromagnetic dynamics of a magnetoelectric system in the presence of an external electric field.

Recent studies have predicted extraordinary properties for transverse domain walls in cylindrical nanowires: zero depinning current, the absence of the Walker breakdown, and applications as domain wall oscillators. In order to reliably control the domain wall motion, it is important to understand how they interact with energy barriers. In this paper, we study the motion and depinning of transverse domain walls through potential barriers in ferromagnetic cylindrical nanowires. We use magnetic fields and spin-polarized currents to drive the domain walls along the wire. Using magnetic fields, we find that the minimum and the maximum fields required to push the domain wall through the barrier differ by 30 %. On the contrary, using spin-polarized currents, we find variations of a factor 130 between the minimum value of the depinning current density and the maximum value. We study the depinning current density as a function of the height of the energy barrier using numerical and analytical methods. We find that, for a barrier of 40 k_B T, a depinning current density of about 5 uA is sufficient to depin the domain wall. We reveal and explain the mechanism that leads to these unusually low depinning currents. One requirement for this new depinning mechanism is for the domain wall to be able to rotate around its own axis. With the right barrier design, the spin torque transfer term is acting exactly against the damping in the micromagnetic system, and thus the low current density is sufficient to accumulate enough energy quickly. These key insights may be crucial in furthering the development of novel memory technologies, such as the racetrack memory, that can be controlled through low current densities., Comment: 9 pages, 10 figures

We present a systematic numerical analysis of the magnetic properties of pyramidal-shaped core-shell structures in a size range below 400 nm. These are three-dimensional structures consisting of a ferromagnetic shell which is grown on top of a non-magnetic core. The standard micromagnetic model without the magnetocrystalline anisotropy term is used to describe the properties of the shell. We vary the thickness of the shell between the limiting cases of an ultra-thin shell and a conventional pyramid and delineate different stable magnetic configurations. We find different kinds of single-domain states, which predominantly occur at smaller system sizes. In analogy to equivalent states in thin square films we term these onion, flower, C and S states. At larger system sizes, we also observe two types of vortex states, which we refer to as symmetric and asymmetric vortex states. For a classification of the observed states, we derive a phase diagram that specifies the magnetic ground state as a function of structure size and shell thickness. The transitions between different ground states can be understood qualitatively. We address the issue of metastability by investigating the stability of all occurring configurations for different shell thicknesses. For selected geometries and directions hysteresis measurements are analysed and discussed. We observe that the magnetic behaviour changes distinctively in the limit of ultra-thin shells. The study has been motivated by the recent progress made in the growth of faceted core-shell structures.

We study the supersymmetric $\mathcal{N}=(2,2)$ Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum-dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called FlowPy. For weak couplings the quantum corrections to the bare mass found in lattice simulations are reproduced with high accuracy. But in the regime with intermediate couplings higher-order operators that are not constrained by the nonrenormalization theorem yield the dominating contribution to the renormalized mass.

The list of six previously known nontrivial stationary points in the scalar potential of N=8, D=4 supergravity with gauge group SO(8) is extended by fourteen new entries, whose properties have been obtained numerically using the sensitivity backpropagation technique. Eight of the new solutions break the gauge group completely, while three have a residual symmetry of U(1). Three further ones break the gauge group to U(1)xU(1), and while the approximate numerical data are somewhat inconclusive, there is evidence that one of these may have a residual N=1 supersymmetry, hence correspond to a stable vacuum. It must be pointed out that this list of new solutions most likely is not exhaustive., 23 pages; typo fixes and some adjustments to text; fermion mass matrix eigenvalues listed

We investigate the consequences of replacing the continuous flavour symmetry of minimal flavour violation by a discrete group. Goldstone bosons, resulting from the breaking of the continuous flavour symmetry, generically lead to bounds on new flavour structure by many orders of magnitude above the TeV-scale. The absence of Goldstone bosons for discrete symmetries constitutes the primary motivation of our work. The four crystal-like groups Sigma(168), Sigma(72phi), Sigma(216phi) and Sigma(360phi)$ provide enough protection for a discrete TeV-scale MFV scenario in the case where Delta F = 2 processes are generated by two subsequent Delta F = 1 transitions., Comment: Presented at Flavianet workshop on "Low energy constraints on extensions of the Standard Model" from 23-27 July 2009 in Kazimierz, Poland and "Progress and Challenges in Flavour Physics" 29 Sep- 3 Oct 2009 in Primosten, Croatia, 7 pages, 1 figure

We present a new method to simulate repetitive ferromagnetic structures. This macrogeometry approach combines treatment of short-range interactions (i.e., the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell in order to correctly include effects of the demagnetizing field. This method (i) solves a consistency problem that prevents the naive application of three-dimensional periodic boundary conditions in micromagnetism and (ii) is well suited for the efficient simulation of repetitive systems of any size.

We demonstrate the feasibility of an ‘encapsulated parallelism’ approach towards micromagnetic simulations that combines offering a high degree of flexibility to the user with the efficient utilization of parallel computing resources.While parallelization is obviously desirable to address the high numerical effort required for realistic micromagnetic simulations through utilizing now widely available multiprocessor systems (including desktop multicore CPUs and computing clusters), conventional approaches towards parallelization impose strong restrictions on the structure of programs: numerical operations have to be executed across all processors in a synchronized fashion. This means that, from the user’s perspective, either the structure of the entire simulation is rigidly defined from the beginning and cannot be adjusted easily, or making modifications to the computation sequence requires advanced knowledge in parallel programming.We explain how this dilemma is resolved in the Nmag simulation package in such a way that the user can utilize without any additional effort on his side both the computational power of multiple CPUs and the flexibility to tailor execution sequences for specific problems: simulation scripts written for single processor machines can just as well be executed on parallel machines and behave in precisely the same way, up to increased speed. We provide a simple instructive magnetic resonance simulation example that demonstrates utilizing both custom execution sequences and parallelism at the same time. Furthermore, we show that this strategy of encapsulating parallelism even allows to benefit from speed gains through parallel execution in simulations controlled by interactive commands given at a command line interface.

We investigate the effects of an electric current on the domain wall formed inside a cylindrical ferromagnetic nanopillar as a consequence of the pinning of the magnetization at its ends. We first present the results of three-dimensional and one-dimensional micromagnetic simulations and show that the system approaches a stationary equilibrium, where the domain wall is compressed in the direction of the electron flow and rotates around the nanopillar axis with constant frequency in the microwave frequency range. We obtain the dependence of the rotation frequency on the length of the nanopillar and on the magnitude of the applied current density. We then introduce a one-dimensional analytical model and find a formula for the rotation frequency in two current regimes: a low current regime, where the frequency is linearly proportional to the current density and a high current regime, where the frequency is quadratically proportional to the current density. Good agreement is found with the results of the simulations. The system may have possible applications as a nanosized microwave generator, which could operate without external magnetic fields and whose emission frequency could be controlled by a dc current.

A novel method is presented which employs advanced numerical techniques used in the engineering sciences to find and study the properties of nontrivial vacua of gauged extended supergravity models. While this method only produces approximate numerical data rather than analytic results, it overcomes the previous limitation of only being able to find vacua with large residual unbroken gauge symmetry groups. The effectiveness of this method is demonstrated by applying it to the technically most challenging D>=3 scalar potential -- that of SO(8) X SO(8) gauged N=16 Chern-Simons Supergravity in D=3. Extensive data on the properties of 99 different vacua (92 of them new) of this model are given. Furthermore, techniques are briefly discussed which should allow using this numerical information as an input to the construction of semi-automatic stringent analytic proofs on the locations and properties of vacua. It hence is argued that these combined techniques presumably are powerful enough to systematically map all the nontrivial vacua of every supergravity model., 66 pages, code to reproduce results can be obtained by downloading paper's source, as described in the text