23 research outputs found
Sugawara-type constraints in hyperbolic coset models
In the conjectured correspondence between supergravity and geodesic models on
infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the
constraints play a central role. We present a Sugawara-type construction in
terms of the E10 Noether charges that extends these constraints infinitely into
the hyperbolic algebra, in contrast to the truncated expressions obtained in
arXiv:0709.2691 that involved only finitely many generators. Our extended
constraints are associated to an infinite set of roots which are all imaginary,
and in fact fill the closed past light-cone of the Lorentzian root lattice. The
construction makes crucial use of the E10 Weyl group and of the fact that the
E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our
extended constraints appear to unite in a remarkable manner the different
canonical constraints of these two theories. This construction may also shed
new light on the issue of `open constraint algebras' in traditional canonical
approaches to gravity.Comment: 49 page
Holography in asymptotically flat space-times and the BMS group
In a previous paper (hep-th/0306142) we have started to explore the
holographic principle in the case of asymptotically flat space-times and
analyzed in particular different aspects of the Bondi-Metzner-Sachs (BMS)
group, namely the asymptotic symmetry group of any asymptotically flat
space-time. We continue this investigation in this paper. Having in mind a
S-matrix approach with future and past null infinity playing the role of
holographic screens on which the BMS group acts, we connect the IR sectors of
the gravitational field with the representation theory of the BMS group. We
analyze the (complicated) mapping between bulk and boundary symmetries pointing
out differences with respect to the AdS/CFT set up. Finally we construct a BMS
phase space and a free hamiltonian for fields transforming w.r.t BMS
representations. The last step is supposed to be an explorative investigation
of the boundary data living on the degenerate null manifold at infinity.Comment: 31 pages, several changes in section 3 and 7 and references update
Black brane solutions related to non-singular Kac-Moody algebras
A multidimensional gravitational model containing scalar fields and
antisymmetric forms is considered. The manifold is chosen in the form M = M_0 x
M_1 x ... x M_n, where M_i are Einstein spaces (i > 0). The sigma-model
approach and exact solutions with intersecting composite branes (e.g.,
solutions with harmonic functions and black brane ones) with intersection rules
related to non-singular Kac-Moody (KM) algebras (e.g. hyperbolic ones) are
considered. Some examples of black brane solutions are presented, e.g., those
corresponding to hyperbolic KM algebras: H_2(q,q) (q > 2), HA_2^(1) = A_2^{++}
and to the Lorentzian KM algebra P_{10}.Comment: 16 pages, Late
Spacelike Singularities and Hidden Symmetries of Gravity
We review the intimate connection between (super-)gravity close to a
spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody
algebras. We show that in this limit the gravitational theory can be
reformulated in terms of billiard motion in a region of hyperbolic space,
revealing that the dynamics is completely determined by a (possibly infinite)
sequence of reflections, which are elements of a Lorentzian Coxeter group. Such
Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras,
suggesting that these algebras yield symmetries of gravitational theories. Our
presentation is aimed to be a self-contained and comprehensive treatment of the
subject, with all the relevant mathematical background material introduced and
explained in detail. We also review attempts at making the infinite-dimensional
symmetries manifest, through the construction of a geodesic sigma model based
on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case
of the hyperbolic algebra E10, which is conjectured to be an underlying
symmetry of M-theory. Illustrations of this conjecture are also discussed in
the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added.
Published versio
From Isotropic to Anisotropic Side Chain Representations: Comparison of Three Models for Residue Contact Estimation
The criterion to determine residue contact is a fundamental problem in deriving knowledge-based mean-force potential energy calculations for protein structures. A frequently used criterion is to require the side chain center-to-center distance or the -to- atom distance to be within a pre-determined cutoff distance. However, the spatially anisotropic nature of the side chain determines that it is challenging to identify the contact pairs. This study compares three side chain contact models: the Atom Distance criteria (ADC) model, the Isotropic Sphere Side chain (ISS) model and the Anisotropic Ellipsoid Side chain (AES) model using 424 high resolution protein structures in the Protein Data Bank. The results indicate that the ADC model is the most accurate and ISS is the worst. The AES model eliminates about 95% of the incorrectly counted contact-pairs in the ISS model. Algorithm analysis shows that AES model is the most computational intensive while ADC model has moderate computational cost. We derived a dataset of the mis-estimated contact pairs by AES model. The most misjudged pairs are Arg-Glu, Arg-Asp and Arg-Tyr. Such a dataset can be useful for developing the improved AES model by incorporating the pair-specific information for the cutoff distance