On the construction of variant supergravities in D=11, D=10

We construct with a geometric procedure the supersymmetry transformation laws and Lagrangian for all the ``variant'' D=11 and D=10 Type IIA supergravities. We identify into our classification the D=11 and D=10 Type IIA ``variant'' theories first introduced by Hull performing T-duality transformation on both spacelike and timelike circles. We find in addition a set of D=10 Type IIA ``variant'' supergravities that can not be obtained trivially from eleven dimensions compactifying on a circle.Comment: 21 pages, Late

Charge Dynamics in Cuprate Superconductors

In this lecture we present some interesting issues that arise when the dynamics of the charge carriers in the CuO$_2$ planes of the high temperature superconductors is considered. Based on the qualitative picture of doping, set by experiments and some previous calculations, we consider the strength of various inter and intra-cell charge transfer susceptibilities, the question of Coulomb screening and charge collective modes. The starting point is the usual p-d model extended by the long range Coulomb (LRC) interaction. Within this model it is possible to examine the case in which the LRC forces frustrate the electronic phase separation, the instability which is present in the model without an LRC interaction. While the static dielectric function in such systems is negative down to arbitrarily small wavevectors, the system is not unstable. We consider the dominant electronic charge susceptibilities and possible consequences for the lattice properties.Comment: 14 pages, 15 figures, latex, to be published in "From Quantum Mechanics to Technology", Lecture Notes in Physics, Springe

Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes

We define and study projective special para-Kahler manifolds and show that they appear as target manifolds when reducing five-dimensional vector multiplets coupled to supergravity with respect to time. The dimensional reductions with respect to time and space are carried out in a uniform way using an epsilon-complex notation. We explain the relation of our formalism to other formalisms of special geometry used in the literature. In the second part of the paper we investigate instanton solutions and their dimensional lifting to black holes. We show that the instanton action, which can be defined after dualising axions into tensor fields, agrees with the ADM mass of the corresponding black hole. The relation between actions via Wick rotation, Hodge dualisation and analytic continuation of axions is discussed.Comment: 72 pages, 2 figure

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Influence of the pseudogap on the superconductivity-induced phonon renormalization in high-Tc_c superconductors

We investigate the influence of a d-density wave (DDW) gap on the superconductivity-induced renormalization of phonon frequency and linewidth. The results are discussed with respect to Raman and inelastic neutron scattering experiments. It turns out that the DDW gap can enhance the range of frequencies for $q=0$ phonon softening depending on the underlying band structure. Moreover we show that an anisotropic 'd-wave' pseudogap can also contribute to the q-dependent linewidth broadening of the 340cm$^{-1}$ phonon in YBa$_2$Cu$_3$O$_7$.Comment: 4 page

Curvatures and potential of M-theory in D=4 with fluxes and twist

We give the curvatures of the free differential algebra (FDA) of M--theory compactified to D=4 on a twisted seven--torus with the 4--form flux switched on. Two formulations are given, depending on whether the 1--form field strengths of the scalar fields (originating from the 3--form gauge field $\hat{A}^{(3)}$) are included or not in the FDA. We also give the bosonic equations of motion and discuss at length the scalar potential which emerges in this type of compactifications. For flat groups we show the equivalence of this potential with a dual formulation of the theory which has the full \rE_{7(7)} symmetry.Comment: 14 pages, LaTeX source, typos correcte

Bond-disordered Anderson model on a two dimensional square lattice - chiral symmetry and restoration of one-parameter scaling

Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at the band center is studied and compared with Gade's result [Nucl. Phys. B 398, 499 (1993)] and the powerlaw. Although Gade's form describes accurately DoS of finite size systems near the band-center, it fails to describe the calculated part of DoS of the infinite system, and a new expression is proposed. Study of the level spacing distributions reveals that the state closest to the band center and the next one have different level spacing distribution than the pairs of states away from the band center. Multifractal properties of finite systems furthermore show that scaling of eigenstates changes discontinuously near the band center. This unusual behavior suggests the existence of a new divergent length scale, whose existence is explained as the finite size manifestation of the band center critical point of the infinite system, and the critical exponent of the correlation length is calculated by a finite size scaling. Furthermore, study of scaling of Lyapunov exponents of transfer matrices of long stripes indicates that for a long stripe of any width there is an energy region around band center within which the Lyapunov exponents cannot be described by one-parameter scaling. This region, however, vanishes in the limit of the infinite square lattice when one-parameter scaling is restored, and the scaling exponent calculated, in agreement with the result of the finite size scaling analysis.Comment: 23 pages, 11 figures. RevTe

Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes

We present the supersymmetric completion of the M-theory free differential algebra resulting from a compactification to four dimensions on a twisted seven-torus with 4-form and 7-form fluxes turned on. The super--curvatures are given and the local supersymmetry transformations derived. Dual formulations of the theory are discussed in connection with classes of gaugings corresponding to diverse choices of vacua. This also includes seven dimensional compactifications on more general spaces not described by group manifolds.Comment: 19 pages, LaTeX, typos corrected, references adde

Influence of incommensurate dynamic charge-density wave scattering on the line shape of high-Tc_c cuprates

We show that the spectral lineshape of superconducting La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) and Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) can be well described by the coupling of the charge carriers to collective incommensurate charge-density wave (CDW) excitations. Our results imply that besides antiferromagnetic (AF) fluctuations also low-energy CDW modes can contribute to the observed dip-hump structure in the Bi2212 photoemission spectra. In case of underdoped LSCO we propose a possible interpretation of ARPES data in terms of a grid pattern of fluctuating stripes where the charge and spin scattering directions deviate by $\alpha=\pi/4$. Within this scenario we find that the spectral intensity along $(0,0) \to (\pi,\pi)$ is strongly suppressed consistent with recent photoemission experiments. In addition the incommensurate charge-density wave scattering leads to a significant broadening of the quasiparticle-peak around $(\pi,0)$.Comment: 5 pages, 4 figure

Special Geometry of Euclidean Supersymmetry I: Vector Multiplets

We construct the general action for Abelian vector multiplets in rigid 4-dimensional Euclidean (instead of Minkowskian) N=2 supersymmetry, i.e., over space-times with a positive definite instead of a Lorentzian metric. The target manifolds for the scalar fields turn out to be para-complex manifolds endowed with a particular kind of special geometry, which we call affine special para-Kahler geometry. We give a precise definition and develop the mathematical theory of such manifolds. The relation to the affine special Kahler manifolds appearing in Minkowskian N=2 supersymmetry is discussed. Starting from the general 5-dimensional vector multiplet action we consider dimensional reduction over time and space in parallel, providing a dictionary between the resulting Euclidean and Minkowskian theories. Then we reanalyze supersymmetry in four dimensions and find that any (para-)holomorphic prepotential defines a supersymmetric Lagrangian, provided that we add a specific four-fermion term, which cannot be obtained by dimensional reduction. We show that the Euclidean action and supersymmetry transformations, when written in terms of para-holomorphic coordinates, take exactly the same form as their Minkowskian counterparts. The appearance of a para-complex and complex structure in the Euclidean and Minkowskian theory, respectively, is traced back to properties of the underlying R-symmetry groups. Finally, we indicate how our work will be extended to other types of multiplets and to supergravity in the future and explain the relevance of this project for the study of instantons, solitons and cosmological solutions in supergravity and M-theory.Comment: 74 page