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A complex symplectic structure on a Lie algebra hh is an integrable complex structure JJ with a closed non-degenerate (2,0)(2,0)-form. It is determined by JJ and the real part ΩΩ of the (2,0)(2,0)-form. Suppose that hh is a semi-direct product g?Vg?V, and both gg and VV are Lagrangian with respect to ΩΩ and totally real with respect to JJ. This note shows that g?Vg?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of ΩΩ and JJ are isomorphic.  相似文献   

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In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a “spin-shell” constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with NN-extended space–time supersymmetry) in three and four space–time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N=1N=1 and BPS-saturated N=2N=2 superparticle actions. We also find the supertwistor form of the action for “spinning particles” with NN-extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N=2N=2 case.  相似文献   

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In this article we study in detail the supersymmetric structures that underlie the system of fermionic zero modes around a superconducting cosmic string. Particularly, we extend the analysis existing in the literature on the one dimensional N=2N=2 supersymmetry and we find multiple N=2N=2, d=1d=1 supersymmetries. In addition, compact perturbations of the Witten index of the system are performed and we find to which physical situations these perturbations correspond. More importantly, we demonstrate that there exists a much more rich supersymmetric structure underlying the system of fermions with NfNf flavors and these are NN-extended supersymmetric structures with non-trivial topological charges, with “NN” depending on the fermion flavors.  相似文献   

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It is shown that four-dimensional N=1N=1 supersymmetric QCD with massive flavors in the fundamental representation of the gauge group can be realized in the hidden sector of E8×E8E8×E8 heterotic string vacua. The number of flavors can be chosen to lie in the range of validity of the free-magnetic dual, using which one can demonstrate the existence of long-lived meta-stable non-supersymmetric vacua. This is shown explicitly for the gauge group Spin(10)Spin(10), but the methods are applicable to Spin(Nc)Spin(Nc), SU(Nc)SU(Nc) and Sp(Nc)Sp(Nc) for a wide range of color index NcNc. Hidden sectors of this type can potentially be used as a mechanism to break supersymmetry within the context of heterotic M-theory.  相似文献   

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Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0T=0 1D insulator the charge stiffness D(T)D(T) vanishes for T>0T>0 and finite values of the on-site repulsion UU in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite TT and U>0U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0U=0 and vanishes for U>0U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0U=Uc=0 for all finite temperatures T>0T>0. (At T=0T=0 such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the ηη-spin SU(2)SU(2) symmetry with the hidden U(1)U(1) symmetry beyond SO(4)SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.  相似文献   

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We investigate the geometry of the moduli space of NN vortices on line bundles over a closed Riemann surface ΣΣ of genus g>1g>1, in the little explored situation where 1≤N<g1N<g. In the regime where the area of the surface is just large enough to accommodate NN vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of ΣΣ. For N=1N=1, we show that the metric on the moduli space converges to a natural Bergman metric on ΣΣ. When N>1N>1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of ΣΣ at degree NN. We describe consequences of this phenomenon from the point of view of multivortex dynamics.  相似文献   

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We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order qq, we first provide a generalized monogamy inequality of multi-qubit entanglement for q=2q=2 or 33. This generalization encapsulates the multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-qq entropy for 1≤q≤21q2 or 3≤q≤43q4, which also contains the multi-qubit polygamy inequality as a special case.  相似文献   

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We discuss three Hamiltonians, each with a central-field part H0H0 and a PT-symmetric perturbation igzigz. When H0H0 is the isotropic Harmonic oscillator the spectrum is real for all gg because HH is isospectral to H0+g2/2H0+g2/2. When H0H0 is the Hydrogen atom then infinitely many eigenvalues are complex for all gg. If the potential in H0H0 is linear in the radial variable rr then the spectrum of HH exhibits real eigenvalues for 0<g<gc0<g<gc and a PT phase transition at gcgc.  相似文献   

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A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞q and infinite equation of state parameter, w→∞w. During evolution it subsequently passes through the stiff fluid era, q=2q=2, w=1w=1, the radiation dominated era, q=1q=1, w=1/3w=1/3 and the matter dominated era, q=1/2q=1/2, w=0w=0. Finally, deceleration halts, q=0q=0, w=−1/3w=1/3, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1q1, w→−1w1. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1)(w<1) the model.  相似文献   

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We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Zp)C(Zp) gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a nn dimensional vector space which we call HnHn. The ZpZp gauge particles act on the vertex particles and thus HnHn can be thought of as a C(Zp)C(Zp) module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of nn and pp, though we believe this feature holds for all n>pn>p. We will see that non-Abelian anyons of the quantum double of C(S3)C(S3) are obtained as part of the vertex excitations of the model with n=6n=6 and p=3p=3. Ising anyons are obtained in the model with n=4n=4 and p=2p=2. The n=3n=3 and p=2p=2 case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than ZpZp. This makes them possible candidates for realizing quantum computation.  相似文献   

17.
We present a method using Feynman-like diagrams to calculate the statistical properties of random many-body potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as the method of supersymmetry and the eigenvector expansion technique pioneered in Benet et al. (2001). We use it here to calculate the fourth, sixth and eighth moments of the average level density for systems with mm bosons or fermions that interact through a random kk-body Hermitian potential (k≤mkm); the ensemble of such potentials with a Gaussian weight is known as the embedded Gaussian Unitary Ensemble   (eGUE) (Mon and French, 1975). Our results apply in the limit where the number ll of available single-particle states is taken to infinity. A key advantage of the method is that it provides an efficient way to identify only those expressions which will stay relevant in this limit. It also provides a general argument for why these terms have to be the same for bosons and fermions. The moments are obtained as sums over ratios of binomial expressions, with a transition from moments associated to a semi-circular level density for m<2km<2k to Gaussian moments in the dilute limit k?m?lk?m?l. Regarding the form of this transition, we see that as mm is increased, more and more diagrams become relevant, with new contributions starting from each of the points m=2k,3k,…,nkm=2k,3k,,nk for the 2n2nth moment.  相似文献   

18.
We study properties of strongly coupled CFT's with non-zero background electric charge in 1+11+1 dimensions by studying the dual gravity theory—which is a charged BTZ black hole. Correlators of operators dual to scalars, gauge fields and fermions are studied at both T=0T=0 and T≠0T0. In the T=0T=0 case we are also able to compare with analytical results based on AdS2AdS2 and find reasonable agreement. In particular the correlation between log periodicity and the presence of finite spectral density of gapless modes is seen. The real part of the conductivity (given by the current–current correlator) also vanishes as ω→0ω0 as expected. The fermion Green's function shows quasiparticle peaks with approximately linear dispersion but the detailed structure is neither Fermi liquid nor Luttinger liquid and bears some similarity to a “Fermi–Luttinger” liquid. This is expected since there is a background charge and the theory is not Lorentz or scale invariant. A boundary action that produces the observed non-Luttinger liquid like behavior (k  -independent non-analyticity at ω=0ω=0) in the Green's function is discussed.  相似文献   

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First of all, we reconsider the tight-binding model of monolayer graphene, in which the variations of the hopping parameters are allowed. We demonstrate that the emergent 2D2D Weitzenbock geometry as well as the emergent U(1)U(1) gauge field appear. The emergent gauge field is equal to the linear combination of the components of the zweibein. Therefore, we actually deal with the gauge fixed version of the emergent 2+12+1   DD teleparallel gravity. In particular, we work out the case, when the variations of the hopping parameters are due to the elastic deformations, and relate the elastic deformations with the emergent zweibein. Next, we investigate the tight-binding model with the varying intralayer hopping parameters for the multilayer graphene with the ABCABC stacking. In this case the emergent 2D2D Weitzenbock geometry and the emergent U(1)U(1) gauge field appear as well, and the emergent low energy effective field theory has the anisotropic scaling.  相似文献   

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