2,643 research outputs found
Noncommutative geometry for three-dimensional topological insulators
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
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 -algebras. Finally
we attack the problem of considering the positivity of , with
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
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
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
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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