2,643 research outputs found

    Noncommutative geometry for three-dimensional topological insulators

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    We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. We provide an example of a model on the cubic lattice for which the chiral symmetry guarantees a macroscopic number of zero-energy modes that form a perfectly flat band. This lattice model realizes a chiral 3D noncommutative geometry. Finally, we find conditions on the density-density structure factors that lead to a gapped 3D fractional chiral topological insulator within Feynman's single-mode approximation.Comment: 41 pages, 3 figure

    Uniformization theory and 2D gravity I. Liouville action and intersection numbers

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    This is the first part of an investigation concerning the formulation of 2D gravity in the framework of the uniformization theory of Riemann surfaces. As a first step in this direction we show that the classical Liouville action appears in the expression of the correlators of topological gravity. Next we derive an inequality involving the cutoff of 2D gravity and the background geometry. Another result, always related to uniformization theory, concerns a relation between the higher genus normal ordering and the Liouville action. Furthermore, we show that the chirally split anomaly of CFT is equivalent to the Krichever-Novikov cocycle. By means of the inverse map of uniformization we give a realization of the Virasoro algebra on arbitrary Riemann surfaces and find the eigenfunctions for {\it holomorphic} covariant operators defining higher order cocycles and anomalies which are related to WW-algebras. Finally we attack the problem of considering the positivity of eσe^\sigma, with σ\sigma the Liouville field, by proposing an explicit construction for the Fourier modes on compact Riemann surfaces.Comment: 53 pages. '95 publ. version, contains Eq.(5.23), independently derived in hep-th/0004194 studying the null compactification of type-IIA-strin

    Theory of Parabolic Arcs in Interstellar Scintillation Spectra

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    Our theory relates the secondary spectrum, the 2D power spectrum of the radio dynamic spectrum, to the scattered pulsar image in a thin scattering screen geometry. Recently discovered parabolic arcs in secondary spectra are generic features for media that scatter radiation at angles much larger than the rms scattering angle. Each point in the secondary spectrum maps particular values of differential arrival-time delay and fringe rate (or differential Doppler frequency) between pairs of components in the scattered image. Arcs correspond to a parabolic relation between these quantities through their common dependence on the angle of arrival of scattered components. Arcs appear even without consideration of the dispersive nature of the plasma. Arcs are more prominent in media with negligible inner scale and with shallow wavenumber spectra, such as the Kolmogorov spectrum, and when the scattered image is elongated along the velocity direction. The arc phenomenon can be used, therefore, to constrain the inner scale and the anisotropy of scattering irregularities for directions to nearby pulsars. Arcs are truncated by finite source size and thus provide sub micro arc sec resolution for probing emission regions in pulsars and compact active galactic nuclei. Multiple arcs sometimes seen signify two or more discrete scattering screens along the propagation path, and small arclets oriented oppositely to the main arc persisting for long durations indicate the occurrence of long-term multiple images from the scattering screen.Comment: 22 pages, 11 figures, submitted to the Astrophysical Journa

    String Creation, D-branes and Effective Field Theory

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    This paper addresses several unsettled issues associated with string creation in systems of orthogonal Dp-D(8-p) branes. The interaction between the branes can be understood either from the closed string or open string picture. In the closed string picture it has been noted that the DBI action fails to capture an extra RR exchange between the branes. We demonstrate how this problem persists upon lifting to M-theory. These D-brane systems are analysed in the closed string picture by using gauge-fixed boundary states in a non-standard lightcone gauge, in which RR exchange can be analysed precisely. The missing piece in the DBI action also manifests itself in the open string picture as a mismatch between the Coleman-Weinberg potential obtained from the effective field theory and the corresponding open string calculation. We show that this difference can be reconciled by taking into account the superghosts in the (0+1)effective theory of the chiral fermion, that arises from gauge fixing the spontaneously broken world-line local supersymmetries.Comment: 33 page

    Generalized moonshine II: Borcherds products

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    The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and Lie algebras. The Lie algebras that we construct conjecturally appear in an orbifold conformal field theory with symmetries given by the monster simple group. We introduce vector-valued modular functions attached to families of modular functions of different levels, and we prove infinite product identities for a distinguished class of automorphic functions on a product of two half-planes. We recast this result using the Borcherds-Harvey-Moore singular theta lift, and show that the vector-valued functions attached to completely replicable modular functions with integer coefficients lift to automorphic functions with infinite product expansions at all cusps. For each element of the monster simple group, we construct an infinite dimensional Lie algebra, such that its denominator formula is an infinite product expansion of the automorphic function arising from that element's McKay-Thompson series. These Lie algebras have the unusual property that their simple roots and all root multiplicities are known. We show that under certain hypotheses, characters of groups acting on these Lie algebras form functions on the upper half plane that are either constant or invariant under a genus zero congruence group.Comment: v3: final version, minor corrections and explanations added, 41 page
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