18,124 research outputs found
A class of Lorentzian Kac-Moody algebras
We consider a natural generalisation of the class of hyperbolic Kac-Moody
algebras. We describe in detail the conditions under which these algebras are
Lorentzian. We also construct their fundamental weights, and analyse whether
they possess a real principal so(1,2) subalgebra. Our class of algebras include
the Lorentzian Kac-Moody algebras that have recently been proposed as
symmetries of M-theory and the closed bosonic string.Comment: 40 pages TeX, 5 eps-figure
Generalised geometry, eleven dimensions and E11
We construct the non-linear realisation of E11 and its first fundamental
representation in eleven dimensions at low levels. The fields depend on the
usual coordinates of space-time as well as two form and five form coordinates.
We derive the terms in the dynamics that contain the three form and six form
fields and show that when we restricted their field dependence to be only on
the usual space-time we recover the correct self-duality relation. Should this
result generalise to the gravity fields then the non-linear realisation is an
extension of the maximal supergravity theory, as previously conjectured. We
also comment on the connections between the different approaches to generalised
geometry.Comment: 17 pages, Trivial typos corrected in version one and a substantial
note added which gives the equation of motion relating the gravity field to
its dua
Duality Symmetries and G^{+++} Theories
We show that the non-linear realisations of all the very extended algebras
G^{+++}, except the B and C series which we do not consider, contain fields
corresponding to all possible duality symmetries of the on-shell degrees of
freedom of these theories. This result also holds for G_2^{+++} and we argue
that the non-linear realisation of this algebra accounts precisely for the form
fields present in the corresponding supersymmetric theory. We also find a
simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables
corrected, other minor changes, one appendix added, refs. added. Version
published in Class. Quant. Gra
The local symmetries of M-theory and their formulation in generalised geometry
In the doubled field theory approach to string theory, the T-duality group is
promoted to a manifest symmetry at the expense of replacing ordinary Riemannian
geometry with generalised geometry on a doubled space. The local symmetries are
then given by a generalised Lie derivative and its associated algebra. This
paper constructs an analogous structure for M-theory. A crucial by-product of
this is the derivation of the physical section condition for M-theory
formulated in an extended space.Comment: 20 pages, v2: Author Name corrected, v3: typos correcte
Generalised Space-time and Gauge Transformations
We consider the generalised space-time introduced by the author in 2003 in
the context of the non-linear realisation of the semi-direct product of E11 and
its first fundamental representation. For all the fields we propose gauge
transformations which are compatible with the underlying E11 structure. A
crucial role is played by the generalised vielbein that the generalised
space-time possess. We work out the explicit form of the gauge transformations,
at low levels, in four, five and eleven dimensions.Comment: 33 page
Duality and the Legendre Transform
We define a weak-strong coupling transformation based on the Legendre
transformation of the effective action. In the case of N\es 2 supersymmetric
Yang-Mills theory, this coincides with the duality transform on the low energy
effective action considered by Seiberg and Witten. This Legendre transform
interpretation of duality generalizes directly to the full effective action,
and in principle to other theories.Comment: 6 pages, LaTe
Zero-Bias Anomalies in Narrow Tunnel Junctions in the Quantum Hall Regime
We report on the study of cleaved-edge-overgrown line junctions with a
serendipitously created narrow opening in an otherwise thin, precise line
barrier. Two sets of zero-bias anomalies are observed with an enhanced
conductance for filling factors and a strongly suppressed conductance
for . A transition between the two behaviors is found near . The zero-bias anomaly (ZBA) line shapes find explanation in
Luttinger liquid models of tunneling between quantum Hall edge states. The ZBA
for occurs from strong backscattering induced by suppression of
quasiparticle tunneling between the edge channels for the Landau
levels. The ZBA for arises from weak tunneling of quasiparticles
between the edge channels.Comment: version with edits for clarit
Worldsheet Matter Superfields on Half-Shell
In this paper we discuss some of the effects of using "unidexterous"
worldsheet superfields, which satisfy worldsheet differential constraints and
so are partly on-shell, i.e., on half-shell. Most notably, this results in a
stratification of the field space that reminds of "brane-world" geometries.
Linear dependence on such superfields provides a worldsheet generalization of
the super-Zeeman effect. In turn, non-linear dependence yields additional
left-right asymmetric dynamical constraints on the propagating fields, again in
a stratified fashion.Comment: 15 pages, 2 figures; minor algebraic correction
Measurements of quasi-particle tunneling in the nu = 5/2 fractional quantum Hall state
Some models of the 5/2 fractional quantum Hall state predict that the
quasi-particles, which carry the charge, have non-Abelian statistics: exchange
of two quasi-particles changes the wave function more dramatically than just
the usual change of phase factor. Such non-Abelian statistics would make the
system less sensitive to decoherence, making it a candidate for implementation
of topological quantum computation. We measure quasi-particle tunneling as a
function of temperature and DC bias between counter-propagating edge states.
Fits to theory give e*, the quasi-particle effective charge, close to the
expected value of e/4 and g, the strength of the interaction between
quasi-particles, close to 3/8. Fits corresponding to the various proposed wave
functions, along with qualitative features of the data, strongly favor the
Abelian 331 state
Multiloop calculations in supersymmetric theories with the higher covariant derivative regularization
Most calculations of quantum corrections in supersymmetric theories are made
with the dimensional reduction, which is a modification of the dimensional
regularization. However, it is well known that the dimensional reduction is not
self-consistent. A consistent regularization, which does not break the
supersymmetry, is the higher covariant derivative regularization. However, the
integrals obtained with this regularization can not be usually calculated
analytically. We discuss application of this regularization to the calculations
in supersymmetric theories. In particular, it is demonstrated that integrals
defining the beta-function are possibly integrals of total derivatives. This
feature allows to explain the origin of the exact NSVZ beta-function, relating
the beta-function with the anomalous dimensions of the matter superfields.
However, integrals for the anomalous dimension should be calculated
numerically.Comment: 8 pages, contribution to ACAT 2011 proceeding
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