914 research outputs found

    BPS and non-BPS Domain Walls in Supersymmetric QCD with SU(3) Gauge Group

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    We study the spectrum of the domain walls interpolating between different chirally asymmetric vacua in supersymmetric QCD with the SU(3) gauge group and including 2 pairs of chiral matter multiplets in fundamental and anti-fundamental representations. For small enough masses m < m* = .286... (in the units of \Lambda), there are two different domain wall solutions which are BPS-saturated and two types of ``wallsome sphalerons''. At m = m*, two BPS branches join together and, in the interval m* < m < m** = 3.704..., BPS equations have no solutions but there are solutions to the equations of motion describing a non-BPS domain wall and a sphaleron. For m > m**, there are no solutions whatsoever.Comment: 10 pages LaTeX, 5 postscript figure

    Noninteger flux - why it does not work

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    We consider the Dirac operator on a 2-sphere without one point in the case of non-integer magnetic flux. We show that the spectral problem for the Hamiltonian (the square of Dirac operator) can always be well defined, if including in the Hilbert space only nonsingular on 2-sphere wave functions. However, this Hilbert space is not invariant under the action of the Dirac operator; the action of the latter on some nonsingular states produces singular functions. This breaks explicitly the supersymmetry of the spectrum. In the integer flux case, the supersymmetry can be restored if extending the Hilbert space to include locally regular sections of the corresponding fiber bundle. For non-integer fluxes, such an extention is not possible.Comment: 10 pages. Eq.(20) correcte

    Proper affine actions on semisimple Lie algebras

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    For any noncompact semisimple real Lie group GG, we construct a group of affine transformations of its Lie algebra g\mathfrak{g} whose linear part is Zariski-dense in Ad⁡G\operatorname{Ad} G and which is free, nonabelian and acts properly discontinuously on g\mathfrak{g}.Comment: Section 3 of this paper draws heavily on the section 3 from my earlier paper arXiv:1303.3766 This is the version that appeared in Geometriae Dedicata. I have corrected some mistakes, added a few examples and added a proof that the Margulis invariant is well-define
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