Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.

MnSb2O6: a polar magnet with a chiral crystal structure

Structural and magnetic chiralities are found to coexist in a small group of materials in which they produce intriguing phenomenologies such as the recently discovered Skyrmion phases. Here, we describe a previously unknown manifestation of this interplay in MnSb2O6, a trigonal oxide with a chiral crystal structure. Unlike all other known cases, the MnSb2O6 magnetic structure is based on corotating cycloids rather than helices. The coupling to the structural chirality is provided by a magnetic axial vector, related to the so-called vector chirality. We show that this unique arrangement is the magnetic ground state of the symmetric-exchange Hamiltonian, based on ab initio theoretical calculations of the Heisenberg exchange interactions, and is stabilized by out-of-plane anisotropy. MnSb2O6 is predicted to be multiferroic with a unique ferroelectric switching mechanism.open4

Contribution of actin filaments and microtubules to cell elongation and alignment depends on the grating depth of microgratings

Additional file 1: Figure S1. (A) A phase contrast image of TCPS surface. Bar, 100 μm. (B) An imageshowing FN-lines (1 μm line and spacing) obtained by Atomic Force Microscopy (AFM) (Dimension 3100with a Nanoscope III controller, Digital Instruments) using silicon cantilevers (spring constant; 50 Nm-1)(RTESP, Veeco Probes) in contact mode. (C-E) SEM (Scanning electron microscopy) (6010 LV, JEOL)images showing the cross section of three different microgratings; 1 μm gratings with 0.35 um depth (C) and1 μm depth (D) and 2 μm gratings with 2 μm depth (E). Figure S2. (A) Fluorescence image of a RPE-1 cell stably expressing GFP/centrin cell on 1 μm gratings (1 μm deep). Bar, 30 μm. A yellow arrow indicates the direction of cell elongation. (B) Average cell aspect ratio (R) of cells on 1 μm gratings (0.35 or 1 μm deep) and 2 μm gratings with/without CD treatment. n: number of cells. ***P < 0.001. Data were analyzed using one-way ANOVA and a Bonferroni post hoc test. Error bar denotes the standard deviation of the mean. Figure S3. Alignment of actin and vinculin to the different substrates (Flat TCPS surface, FN-lines, and 1 μm gratings (0.35 or 1μm deep)). The alignment angle was measured as an angle difference of actin or vinculin orientation to the long axis of a cell on flat PDMS surface or the long axis of the FN-line or each micrograting. #: the number of cells. Error bar denotes the standard deviation of the mean. Figure S4. Merged image of MTs (Green fluorescence) and pattern (phase contrast) of cells on 1 μm grating (1 μm deep) in the presenceof CD at 1 μM

Strong magnetoelastic effect on the magnetoelectric phenomena of TbMn2O5

Comparative studies of magnetoelectric susceptibility (??), magnetization (M), and magnetostriction (u) in TbMn2O5 reveal that the increment of M owing to the field-induced Tb3+ spin alignment produces a field-asymmetric line shape in the ??(H) curve, which is conspicuous in a low-temperature incommensurate phase but persistently subsists in the entire ferroelectric phase. Correlations among electric polarization, u, and M2 variation represent linear relationships, unambiguously showing the significant role of Tb magnetoelastic effects on the low-field magnetoelectric phenomena of TbMn2O5. An effective free energy capturing the observed experimental features is also suggested.open3

Photoemission and x-ray absorption study of MgC_(1-x)Ni_3

We investigated electronic structure of MgC_(1-x)Ni_3 with photoemission and x-ray absorption spectroscopy. Both results show that overall band structure is in reasonable agreement with band structure calculations including the existence of von Hove singularity (vHs)near E_F. However, we find that the sharp vHs peak theoretically predicted near the E_F is substantially suppressed. As for the Ni core level and absorption spectrum, there exist the satellites of Ni 2p which have a little larger energy separation and reduced intensity compared to the case of Ni-metal. These facts indicate that correlation effects among Ni 3d electrons may be important to understand various physical properties.Comment: 12 pages, 4 figure

Towards A Background Independent Quantum Gravity

We recapitulate the scheme of emergent gravity to highlight how a background independent quantum gravity can be defined by quantizing spacetime itself.Comment: 25 pages, 2 figures, Proceedings of 7th International Conference "Quantum Theory and Symmetries" (QTS-7) in Prague, Czech Republic, August, 201

An Efficient Representation of Euclidean Gravity I

We explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to prove that a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons and SU(2)_R anti-instantons where SU(2)_L and SU(2)_R are normal subgroups of the four-dimensional Lorentz group Spin(4) = SU(2)_L x SU(2)_R. Our proof relies only on the general properties in four dimensions: The Lorentz group Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space of two-forms splits canonically into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms. Consolidating these two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-manifold which occupies a central position in the theory of four-manifolds.Comment: 31 pages, 1 figur

N=8 SCFT and M Theory on AdS_4 x RP^7

We study M theory on AdS_4 \times \RP^7 corresponding to 3 dimensional ${\cal N}=8$ superconformal field theory which is the strong coupling limit of 3 dimensional super Yang-Mills theory. For SU(N) theory, a wrapped M5 brane on \RP^5 can be interpreted as baryon vertex. For $SO(N)/Sp(2N)$ theory, by using the property of (co-)homology of \RP^7, we classify various wrapping branes and consider domain walls and the baryon vertex.Comment: 17 pages, Changed baryon like operator as M5 branes in M theory rather than D6 brane in IIA theory. To appear in Phys.Rev.

Spontaneous Eosinophilic Nasal Inflammation in a Genetically-Mutant Mouse: Comparative Study with an Allergic Inflammation Model

Background: Eosinophilic inflammation is a hallmark of chronic rhinosinusitis with nasal polyps. To model this disease process experimentally, nasal sensitization of mice with ovalbumin or aspergillus has been described. Here, we describe a genetically mutant mouse that develops robust spontaneous nasal eosinophilic inflammation. These mice lack the enzyme SHP-1 that down-regulates the IL-4Ra/stat6 signaling pathway. We compared nasal inflammation and inflammatory mediators in SHP-1 deficient mice (mev) and an ovalbumin-induced nasal allergy model. Methods: A novel technique of trans-pharyngeal nasal lavage was developed to obtain samples of inflammatory cells from the nasal passages of allergic and mev mice. Total and differential cell counts were performed on cytospin preparations. Expression of tissue mRNA for IL-4, IL-13, and mouse beta-defensin-1 (MBD-1) was determined by quantitative PCR. Eotaxin in the lavage fluid was assessed by ELISA. Results: Allergic and mev mice had increased total cells and eosinophils compared with controls. Expression of IL-4 was similarly increased in both allergic and mev mice, but expression of IL-13 and eotaxin was significantly greater in the allergic mice than mev mice. Eotaxin was significantly up-regulated in both allergic rhinitis and mev mice. In both models of eosinophilic inflammation, down-regulation of the innate immune marker MBD-1 was observed. Conclusions: The mev mice display spontaneous chronic nasal eosinophilic inflammation with potential utility for chroni