458 research outputs found
The many vacua of gauged extended supergravities
No full textA novel method is presented which employs advanced numerical techniquesused in the engineering sciences to find and study the properties of nontrivialvacua of gauged extended supergravity models. While this method only producesapproximate numerical data rather than analytic results, it overcomes the previouslimitation of only being able to find vacua with large residual unbroken gauge symmetrygroups. The effectiveness of this method is demonstrated by applying it to thetechnically most challenging D ? 3 scalar potential—that of SO(8) × SO(8) gaugedN = 16 Chern–Simons Supergravity in D = 3. Extensive data on the properties of99 different vacua (92 of them new) of this model are given. Furthermore, techniquesare briefly discussed which should allow using this numerical information as an inputto the construction of semi-automatic stringent analytic proofs on the locations andproperties of vacua. It hence is argued that these combined techniques presumably arepowerful enough to systematically map all the nontrivial vacua of every supergravitymodel
Fourteen new stationary points in the scalar potential of SO(8)-gauged N=8, D=4 supergravity
No full textThe 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 exhaustiv
Mapping the vacuum structure of gauged maximal supergravities: an application of high performance symbolic algebra
No full textThe analysis of the extremal structure of the scalar potentials of gauged maximally extended supergravity models in five, four, and three dimensions, and hence the determination of possible vacuum states of these models is a computationally challenging task due to the occurrence of the exceptional Lie groups , , in the definition of these potentials. At present, the most promising approach to gain information about nontrivial vacua of these models is to perform a truncation of the potential to submanifolds of the coset manifold of scalars which are invariant under a subgroup of the gauge group and of sufficiently low dimension to make an analytic treatment possible.
New tools are presented which allow a systematic and highly effective study of these potentials up to a previously unreached level of complexity. Explicit forms of new truncations of the potentials of four- and three-dimensional models are given, and for N=16, D=3 supergravities, which are much more rich in structure than their higher-dimensional cousins, a series of new nontrivial vacua is identified and analyse
Joule heating in nanowires
No full textWe study the effect of Joule heating from electric currents flowing through ferromagnetic nanowires on the temperature of the nanowires and on the temperature of the substrate on which the nanowires are grown. The spatial current density distribution, the associated heat generation, and diffusion of heat is simulated within the nanowire and the substrate. We study several different nanowire and constriction geometries as well as different substrates: (thin) silicon nitride membranes, (thick) silicon wafers, and (thick) diamond wafers. The spatially resolved increase in temperature as a function of time is computed. For effectively three-dimensional substrates (where the substrate thickness greatly exceeds the nanowire length), we identify three different regimes of heat propagation through the substrate: regime (i), where the nanowire temperature increases approximately logarithmically as a function of time. In this regime, the nanowire temperature is well-described analytically by You et al. [APL89, 222513 (2006)]. We provide an analytical expression for the time tc that marks the upper applicability limit of the You model. After tc, the heat flow enters regime (ii), where the nanowire temperature stays constant while a hemispherical heat front carries the heat away from the wire and into the substrate. As the heat front reaches the boundary of the substrate, regime (iii) is entered where the nanowire and substrate temperature start to increase rapidly. For effectively two-dimensional substrates (where the nanowire length greatly exceeds the substrate thickness), there is only one regime in which the temperature increases logarithmically with time for large times. We provide an analytical expression, valid for all pulse durations, that allows one to accurately compute this temperature increase in the nanowire on thin substrate
The structure of E(10) at higher A(9) levels: a first algorithmic approach
No full textThe conjecture of a hidden E10 symmetry of M-theory is supported by the close connection between the dynamics of D = 11 supergravity near a spacelike singularity and a truncation of an one-dimensional ?-model with E10 symmetry where all representations beyond SL(10) level ell = 3 are omitted. If this conjecture is right, higher-level representations should especially capture the dynamics of further M-theory degrees of freedom. Unfortunately, the level by level determination of E10 commutators which is necessary to extend the model to higher levels is both an involved and toilsome task that requires computer aid. In this work, some of the relevant problems are exposed and algorithmic methods are developed which simplify key steps in the determination of explicit E10 commutators at higher levels. As an application, we compute the commutator of the level-two six-form with itsel
Discrete minimal flavour violation
No full textWe investigate the consequences of replacing the global flavor symmetry of minimal flavor violation (MFV) SU(3)Q×SU(3)U×SU(3)D×[centered ellipsis] by a discrete [script D]Q×[script D]U×[script D]D×[centered ellipsis] symmetry. Goldstone bosons resulting from the breaking of the flavor symmetry generically lead to bounds on new flavor structure many orders of magnitude above the TeV scale. The absence of Goldstone bosons for discrete symmetries constitute the primary motivation of our work. Less symmetry implies further invariants and renders the mass-flavor basis transformation observable in principle and calls for a hierarchy in the Yukawa matrix expansion. We show, through the dimension of the representations, that the (discrete) symmetry in principle does allow for additional DeltaF=2 operators. If though the DeltaF=2 transitions are generated by two subsequent DeltaF=1 processes, as, for example, in the standard model, then the four crystal-like groups Sigma(168)[approximate]PSL(2,[openface F]7), Sigma(72phi), Sigma(216phi) and especially Sigma(360phi) do provide enough protection for a TeV-scale discrete MFV scenario. Models where this is not the case have to be investigated case by case. Interestingly Sigma(216phi) has a (nonfaithful) representation corresponding to an A4 symmetry. Moreover we argue that the, apparently often omitted, (D) groups are subgroups of an appropriate Delta(6g2). We would like to stress that we do not provide an actual model that realizes the MFV scenario nor any other theory of flavor
Domain wall motion in perpendicular anisotropy nanowires with edge roughness
No full textWe study field-driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy using finite element micromagnetic simulations. Edge roughness is introduced by deforming the finite element mesh, and we vary the correlation length and magnitude of the roughness deformation separately. We observe the Walker breakdown both with and without roughness, with steady DW motion for applied fields below the critical Walker field Hc, and oscillatory motion for larger fields. The value of Hc is not altered in the presence of roughness.The edge roughness introduces a depinning field. During the transient process of depinning, from the initial configuration to steady DW motion, the DW velocity is significantly reduced in comparison to that for a wire without roughness. The asymptotic DW velocity, on the other hand, is virtually unaffected by the roughness, even though the magnetization reacts to the edge distortions during the entire course of motion, both above and below the Walker breakdown.A moving DW can become pinned again at some later point ('dynamic pinning'). Dynamic pinning is a stochastic process and is observed both for small fields below Hc and for fields of any strength above Hc. In the latter case, where the DW shows oscillatory motion and the magnetization in the DW rotates in the film plane, pinning can only occur at positions where the DW reverses direction and the instantaneous velocity is zero, i.e., at the beginning or in the middle of a positional oscillation cycle. In our simulations pinning was only observed at the beginnings of cycles, where the magnetization is pointing along the wire.The depinning field depends linearly on the magnitude of the edge roughness. The strongest pinning fields are observed for roughness correlation lengths that match the domain wall width
Planar plane-wave matrix theory at the four loop order: integrability without BMN scaling
No full textWe study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective hamiltonian in the closed fraktur sfraktur u(2) subsector of the model is explicitly computed through a specially tailored computer program to perform large scale distributed symbolic algebra and generation of planar graphs. The number of graphs here was in the deep billions. The outcome of our computation establishes the four-loop integrability of the planar plane-wave matrix model. To elucidate the integrable structure we apply the recent technology of the perturbative asymptotic Bethe ansatz to our model. The resulting S-matrix turns out to be structurally similar but nevertheless distinct to the so far considered long-range spin-chain S-matrices of Inozemtsev, Beisert-Dippel-Staudacher and Arutyunov-Frolov-Staudacher in the AdS/CFT context. In particular our result displays a breakdown of BMN scaling at the four-loop order. That is, while there exists an appropriate identification of the matrix theory mass parameter with the coupling constant of the Script N = 4 superconformal Yang-Mills theory which yields an eighth order lattice derivative for well separated impurities (naively implying BMN scaling) the detailed impurity contact interactions ruin this scaling property at the four-loop order. Moreover we study the issue of "wrapping" interactions, which show up for the first time at this loop-order through a Konishi descendant length four operato
Bulk Witten indices from D=10 Yang-Mills integrals
No full textValues for the bulk Witten indices for D=10 Yang-Mills integrals for some regular simple groups of rank 4 and 5 are calculated by employing the BRST deformation technique by Moore, Nekrasov and Shatashvili. The results cannot be reconciled with the double assumption that the number of normalizable ground states is given by certain simple partition functions given by Kac and Smilga as well as that the corresponding boundary term is always negativ
Some stationary points of gauged N=16 D=3 supergravity
No full textFive nontrivial stationary points are found for maximal gauged N=16 supergravity in three dimensions with gauge group SO(8)xSO(8) by restricting the potential to a submanifold of the space of SU(3)C(SO(8)xSO(8) diag singlets. The construction presented here uses the embedding of E_{7(+7)CE8(+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
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