52,705 research outputs found

    On Artin algebras arising from Morita contexts

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    We study Morita rings \Lambda_{(\phi,\psi)}=\bigl({smallmatrix} A &_AN_B_BM_A & B {smallmatrix}\bigr) in the context of Artin algebras from various perspectives. First we study covariant finite, contravariant finite, and functorially finite subcategories of the module category of a Morita ring when the bimodule homomorphisms ϕ\phi and ψ\psi are zero. Further we give bounds for the global dimension of a Morita ring Λ(0,0)\Lambda_{(0,0)}, regarded as an Artin algebra, in terms of the global dimensions of AA and BB in the case when both ϕ\phi and ψ\psi are zero. We illustrate our bounds with some examples. Finally we investigate when a Morita ring is a Gorenstein Artin algebra and then we determine all the Gorenstein-projective modules over the Morita ring with A=N=M=B=ΛA=N=M=B=\Lambda, where Λ\Lambda is an Artin algebra.Comment: 29 pages, revised versio

    Instrument quickly transposes ground reference target to eye level

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    Optical alignment of equipment is facilitated by a traverse target with a string suspending a plumb bob to transpose the ground level point to eye level operation. This instrument appreciably decreases the time required from the present method but achieves the same degree of precision

    Electron paramagnetic resonance and photochromism of N3V0\mathrm{N}_{3}\mathrm{V}^{0} in diamond

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    The defect in diamond formed by a vacancy surrounded by three nearest-neighbor nitrogen atoms and one carbon atom, N3V\mathrm{N}_{3}\mathrm{V}, is found in ≈98%\approx98\% of natural diamonds. Despite N3V0\mathrm{N}_{3}\mathrm{V}^{0} being the earliest electron paramagnetic resonance spectrum observed in diamond, to date no satisfactory simulation of the spectrum for an arbitrary magnetic field direction has been produced due to its complexity. In this work, N3V0\mathrm{N}_{3}\mathrm{V}^{0} is identified in 15N^{15}\mathrm{N}-doped synthetic diamond following irradiation and annealing. The 15N3V0\mathrm{^{15}N}_{3}\mathrm{V}^{0} spin Hamiltonian parameters are revised and used to refine the parameters for 14N3V0\mathrm{^{14}N}_{3}\mathrm{V}^{0}, enabling the latter to be accurately simulated and fitted for an arbitrary magnetic field direction. Study of 15N3V0\mathrm{^{15}N}_{3}\mathrm{V}^{0} under excitation with green light indicates charge transfer between N3V\mathrm{N}_{3}\mathrm{V} and Ns\mathrm{N_s}. It is argued that this charge transfer is facilitated by direct ionization of N3V−\mathrm{N}_{3}\mathrm{V}^{-}, an as-yet unobserved charge state of N3V\mathrm{N}_{3}\mathrm{V}

    Maximal supersymmetry and exceptional groups

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    The article is a tribute to my old mentor, collaborator and friend Murray Gell-Mann. In it I describe work by Pierre Ramond, Sung-Soo Kim and myself where we describe the N = 8 Supergravity in the light-cone formalism. We show how the Cremmer-Julia E7(7) non-linear symmetry is implemented and how the full supermultiplet is a representation of the E7(7) symmetry. I also show how the E7(7) symmetry is a key to understand the higher order couplings in the theory and is very useful when we discuss possible counterterms for this theory.Comment: Proceedings of Conference in Honour of Murray Gell-Mann's 80th Birthda

    String Bit Models for Superstring

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    We extend the model of string as a polymer of string bits to the case of superstring. We mainly concentrate on type II-B superstring, with some discussion of the obstacles presented by not II-B superstring, together with possible strategies for surmounting them. As with previous work on bosonic string we work within the light-cone gauge. The bit model possesses a good deal less symmetry than the continuous string theory. For one thing, the bit model is formulated as a Galilei invariant theory in (D−2)+1(D-2)+1 dimensional space-time. This means that Poincar\'e invariance is reduced to the Galilei subgroup in D−2D-2 space dimensions. Naturally the supersymmetry present in the bit model is likewise dramatically reduced. Continuous string can arise in the bit models with the formation of infinitely long polymers of string bits. Under the right circumstances (at the critical dimension) these polymers can behave as string moving in DD dimensional space-time enjoying the full N=2N=2 Poincar\'e supersymmetric dynamics of type II-B superstring.Comment: 43 pages, phyzzx require

    The Standard Model on a D-brane

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    We present a consistent string theory model which reproduces the Standard Model, consisting of a D3-brane at a simple orbifold singularity. We study some simple features of the phenomenology of the model. We find that the scale of stringy physics must be in the multi-TeV range. There are natural hierarchies in the fermion spectrum and there are several possible experimental signatures of the model.Comment: 8 pages Latex, 1 fig. v2: discussion improved, added new reference

    Perturbative Relations between Gravity and Gauge Theory

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    We review the relations that have been found between multi-loop scattering amplitudes in gauge theory and gravity, and their implications for ultraviolet divergences in supergravity.Comment: LaTex with package axodraw.sty. 10 pages. Presented by L.D. at Strings 99. Cosmetic changes onl

    Remarks on the Classical Size of D-Branes

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    We discuss different criteria for `classical size' of extremal Dirichlet p-branes in type-II supergravity. Using strong-weak coupling duality, we find that the size of the strong-coupling region at the core of the (p<3)-branes, is always given by the asymptotic string scale, if measured in the weakly coupled dual string metric. We also point out how the eleven-dimensional Planck scale arises in the classical 0-brane solution, as well as the ten-dimensional Planck scale in the D-instanton solution.Comment: 8 pp, harvma

    Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude

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    The Type II Superstring amplitude to 1-loop order is given by an integral of ϑ\vartheta-functions over the moduli space of tori, which diverges for real momenta. We construct the analytic continuation which renders this amplitude well defined and finite, and we find the expected poles and cuts in the complex momentum plane.Comment: 10pp, /UCLA/93/TEP/
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