12 research outputs found
From Dynkin diagram symmetries to fixed point structures
Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra
induces an automorphism of the algebra and a mapping between its highest weight
modules. For a large class of such Dynkin diagram automorphisms, we can
describe various aspects of these maps in terms of another Kac-Moody algebra,
the `orbit Lie algebra'. In particular, the generating function for the trace
of the map on modules, the `twining character', is equal to a character of the
orbit Lie algebra. Orbit Lie algebras and twining characters constitute a
crucial step towards solving the fixed point resolution problem in conformal
field theory.Comment: Latex, 60 pages (extended version 63 pages), 4 uuencoded figures
Formula (6.25) corrected. While this correction might be important in
applications of our work, the results of the paper are not affected by it. In
the present submission the "extended version" is default. In this version the
corrected formula is (6.32
Fake R^4's, Einstein Spaces and Seiberg-Witten Monopole Equations
We discuss the possible relevance of some recent mathematical results and
techniques on four-manifolds to physics. We first suggest that the existence of
uncountably many R^4's with non-equivalent smooth structures, a mathematical
phenomenon unique to four dimensions, may be responsible for the observed
four-dimensionality of spacetime. We then point out the remarkable fact that
self-dual gauge fields and Weyl spinors can live on a manifold of Euclidean
signature without affecting the metric. As a specific example, we consider
solutions of the Seiberg-Witten Monopole Equations in which the U(1) fields are
covariantly constant, the monopole Weyl spinor has only a single constant
component, and the 4-manifold M_4 is a product of two Riemann surfaces
Sigma_{p_1} and Sigma_{p_2}. There are p_{1}-1(p_{2}-1) magnetic(electric)
vortices on \Sigma_{p_1}(\Sigma_{p_2}), with p_1 + p_2 \geq 2 (p_1=p_2= 1 being
excluded). When the two genuses are equal, the electromagnetic fields are
self-dual and one obtains the Einstein space \Sigma_p x \Sigma_p, the monopole
condensate serving as the cosmological constant.Comment: 9 pages, Talk at the Second Gursey Memorial Conference, June 2000,
Istanbu
Gravitational Instantons from Minimal Surfaces
Physical properties of gravitational instantons which are derivable from
minimal surfaces in 3-dimensional Euclidean space are examined using the
Newman-Penrose formalism for Euclidean signature. The gravitational instanton
that corresponds to the helicoid minimal surface is investigated in detail.
This is a metric of Bianchi Type , or E(2) which admits a hidden
symmetry due to the existence of a quadratic Killing tensor. It leads to a
complete separation of variables in the Hamilton-Jacobi equation for geodesics,
as well as in Laplace's equation for a massless scalar field. The scalar Green
function can be obtained in closed form which enables us to calculate the
vacuum fluctuations of a massless scalar field in the background of this
instanton.Comment: One figure available by fax upon request. Abstract missing in
original submission. Submitted to Classical and Quantum Gravit
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
An open bosonic string with one end fixed
We study a bosonic string with one end free and the other confined to a D-brane. Only the odd oscillator modes are allowed, which leads to a Virasoro algebra of even Virasoro modes only. The theory is quantized in a gauge where world-sheet time and ordinary time are identified. There are no negative or null norm states, and no tachyon. The Regge slope is twice that of the open string; this can serve as a test of the usefulness of the the model as a semi-quantitative description of mesons with one light and one extremely heavy quark when such higher spin mesons are found. The Virasoro conditions select specific SO(D-1) irreps. The asymptotic density of states can be estimated by adapting the Hardy-Ramanujan analysis to a partition of odd integers; the estimate becomes exact as D goes to infinity
An open bosonic string with one end fixed
We study a bosonic string with one end free and the other confined to a D-brane. Only the odd oscillator modes are allowed, which leads to a Virasoro algebra of even Virasoro modes only. The theory is quantized in a gauge where world-sheet time and ordinary time are identified. There are no negative or null norm states, and no tachyon. The Regge slope is twice that of the open string; this can serve as a test of the usefulness of the the model as a semi-quantitative description of mesons with one light and one extremely heavy quark when such higher spin mesons are found. The Virasoro conditions select specific SO(D-1) irreps. The asymptotic density of states can be estimated by adapting the Hardy-Ramanujan analysis to a partition of odd integers; the estimate becomes exact as D goes to infinity
Yang-Mills strings, Painleve-Liouville and Ernst equations and Gibbsons-Hawking metrics
SIGLEDEGerman
An open bosonic string with one end fixed
We study a bosonic string with one end free and the other confined to a D-brane. Only the odd oscillator modes are allowed, which leads to a Virasoro algebra of even Virasoro modes only. The theory is quantized in a gauge where world-sheet time and ordinary time are identified. There are no negative or null norm states, and no tachyon. The Regge slope is twice that of the open string; this can serve as a test of the usefulness of the the model as a semi-quantitative description of mesons with one light and one extremely heavy quark when such higher spin mesons are found. The Virasoro conditions select specific SO(D-1) irreps. The asymptotic density of states can be estimated by adapting the Hardy-Ramanujan analysis to a partition of odd integers; the estimate becomes exact as D goes to infinity