G(2) quivers

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of Script N = 1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered

A Two-dimensional Superconductor in a Tilted Magnetic Field - new states with finite Cooper-pair momentum

Varying the angle Theta between applied field and the conducting planes of a layered superconductor in a small interval close to the plane-parallel field direction, a large number of superconducting states with unusual properties may be produced. For these states, the pair breaking effect of the magnetic field affects both the orbital and the spin degree of freedom. This leads to pair wave functions with finite momentum, which are labeled by Landau quantum numbers 0<n<\infty. The stable order parameter structure and magnetic field distribution for these states is found by minimizing the quasiclassical free energy near H_{c2} including nonlinear terms. One finds states with coexisting line-like and point-like order parameter zeros and states with coexisting vortices and antivortices. The magnetic response may be diamagnetic or paramagnetic depending on the position within the unit cell. The structure of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states at Theta=0 is reconsidered. The transition n->\infty of the paramagnetic vortex states to the FFLO-limit is analyzed and the physical reason for the occupation of higher Landau levels is pointed out.Comment: 24 pages, 11 figure

Super-Hubbard models and applications

We construct XX- and Hubbard- like models based on unitary superalgebras gl(N|M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N|M) XX model and that of the Hubbard model defined by coupling two independent XX models. In both cases, we show that the R-matrices satisfy the Yang--Baxter equation, we derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine the symmetry of the Hamiltonian. Explicit examples are worked out. In the cases of the gl(1|2) and gl(2|2) Hubbard models, a perturbative calculation at two loops a la Klein and Seitz is performed.Comment: 26 page

Quantized bulk fermions in the Randall-Sundrum brane model

The lowest order quantum corrections to the effective action arising from quantized massive fermion fields in the Randall-Sundrum background spacetime are computed. The boundary conditions and their relation with gauge invariance are examined in detail. The possibility of Wilson loop symmetry breaking in brane models is also analysed. The self-consistency requirements, previously considered in the case of a quantized bulk scalar field, are extended to include the contribution from massive fermions. It is shown that in this case it is possible to stabilize the radius of the extra dimensions but it is not possible to simultaneously solve the hierarchy problem, unless the brane tensions are dramatically fine tuned, supporting previous claims.Comment: 25 pages, 1 figure, RevTe

Quantum geometrodynamics: whence, whither?

Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.Comment: 25 pages; invited contribution for the Proceedings of the seminar "Quantum Gravity: Challenges and Perspectives", Bad Honnef, Germany, April 200

Influence of orbital pair breaking on paramagnetically limited states in clean superconductors

Paramagnetic pair breaking is believed to be of increasing importance in many layered superconducting materials such as cuprates and organic compounds. Recently, strong evidence for a phase transition to the Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) state has been obtained for the first time. We present a new theory of competing spin and orbital pair breaking in clean superconducting films or layers. As a general result, we find that the influence of orbital pair breaking on the paramagnetically limited phase boundary is rather strong, and its neglect seldom justified. This is particularly true for the FFLO state which can be destroyed by a very small orbital contribution. We discuss the situation in YBa_2Cu_3O_7 which has two coupled conducting Cu-O layers per unit cell. As a consequence, an intrinsic orbital pair breaking component might exist even for applied field exactly parallel to the layers.Comment: 19 pages, 5 figures, submitted to PR

The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9

Tomato: a crop species amenable to improvement by cellular and molecular methods

Tomato is a crop plant with a relatively small DNA content per haploid genome and a well developed genetics. Plant regeneration from explants and protoplasts is feasable which led to the development of efficient transformation procedures. In view of the current data, the isolation of useful mutants at the cellular level probably will be of limited value in the genetic improvement of tomato. Protoplast fusion may lead to novel combinations of organelle and nuclear DNA (cybrids), whereas this technique also provides a means of introducing genetic information from alien species into tomato. Important developments have come from molecular approaches. Following the construction of an RFLP map, these RFLP markers can be used in tomato to tag quantitative traits bred in from related species. Both RFLP's and transposons are in the process of being used to clone desired genes for which no gene products are known. Cloned genes can be introduced and potentially improve specific properties of tomato especially those controlled by single genes. Recent results suggest that, in principle, phenotypic mutants can be created for cloned and characterized genes and will prove their value in further improving the cultivated tomato.

Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes

We investigate orientifolds of type II string theory on K3 and Calabi-Yau 3-folds with intersecting D-branes wrapping special Lagrangian cycles. We determine quite generically the chiral massless spectrum in terms of topological invariants and discuss both orbifold examples and algebraic realizations in detail. Intriguingly, the developed techniques provide an elegant way to figure out the chiral sector of orientifold models without computing any explicit string partition function. As a new example we derive a non-supersymmetric Standard-like Model from an orientifold of type IIA on the quintic Calabi-Yau 3-fold with wrapped D6-branes. In the case of supersymmetric intersecting brane models on Calabi-Yau manifolds we discuss the D-term and F-term potentials, the effective gauge couplings and the Green-Schwarz mechanism. The mirror symmetric formulation of this construction is provided within type IIB theory. We finally include a short discussion about the lift of these models from type IIB on K3 to F-theory and from type IIA on Calabi-Yau 3-folds to M-theory on G_2 manifolds.Comment: 82 pages, harvmac, 5 figures. v2: references added. v3: T^6 orientifold corrected, JHEP versio

Transport properties of strongly correlated metals:a dynamical mean-field approach

The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling are calculated. Dynamical mean-field theory, which maps the Hubbard model onto a single impurity Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. This crossover leads to a non-monotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. The resistance smoothly increases from a quadratic temperature dependence at low temperatures to large values which can exceed the Mott-Ioffe-Regel value, hbar a/e^2 (where "a" is a lattice constant) associated with mean-free paths less than a lattice constant. Further signatures of the thermal destruction of quasiparticle excitations are a peak in the thermopower and the absence of a Drude peak in the optical conductivity. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals.Comment: 19 pages, 9 eps figure