740 research outputs found
Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation
We present a class of three-dimensional integrable structures associated with
the Darboux-Egoroff metric and classical Euler equations of free rotations of a
rigid body. They are obtained as canonical structures of rational
Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.Comment: 20 page
Symetric Monopoles
We discuss Bogomolny monopoles of arbitrary charge invariant
under various symmetry groups. The analysis is largely in terms of the spectral
curves, the rational maps, and the Nahm equations associated with monopoles. We
consider monopoles invariant under inversion in a plane, monopoles with cyclic
symmetry, and monopoles having the symmetry of a regular solid. We introduce
the notion of a strongly centred monopole and show that the space of such
monopoles is a geodesic submanifold of the monopole moduli space.
By solving Nahm's equations we prove the existence of a tetrahedrally
symmetric monopole of charge and an octahedrally symmetric monopole of
charge , and determine their spectral curves. Using the geodesic
approximation to analyse the scattering of monopoles with cyclic symmetry, we
discover a novel type of non-planar -monopole scattering process
Yang-Mills equation for stable Higgs sheaves
We establish a Kobayashi-Hitchin correspondence for the stable Higgs sheaves
on a compact Kaehler manifold. Using it, we also obtain a Kobayashi-Hitchin
correspondence for the stable Higgs G-sheaves, where G is any complex reductive
linear algebraic group
The Phase Structure of Mass-Deformed SU(2)xSU(2) Quiver Theory
The phase structure of the finite SU(2)xSU(2) theory with N=2 supersymmetry,
broken to N=1 by mass terms for the adjoint-valued chiral multiplets, is
determined exactly by compactifying the theory on a circle of finite radius.
The exact low-energy superpotential is constructed by identifying it as a
linear combination of the Hamiltonians of a certain symplectic reduction of the
spin generalized elliptic Calogero-Moser integrable system. It is shown that
the theory has four confining, two Higgs and two massless Coulomb vacua which
agrees with a simple analysis of the tree-level superpotential of the
four-dimensional theory. In each vacuum, we calculate all the condensates of
the adjoint-valued scalars.Comment: 12 pages, JHEP.cl
Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation
Hidden symmetries in a covariant Hamiltonian formulation are investigated
involving gauge covariant equations of motion. The special role of the
Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce
the original phase space to another one in which the symmetries are divided
out. The reverse of the reduction procedure is done by stages performing the
unfolding of the gauge transformation followed by the Eisenhart lift in
connection with scalar potentials.Comment: 15 pages; based on a talk at QTS-7 Conference, Prague, August 7-13,
201
Compact Einstein Spaces based on Quaternionic K\"ahler Manifolds
We investigate the Einstein equation with a positive cosmological constant
for -dimensional metrics on bundles over Quaternionic K\"ahler base
manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein
equations are reduced to a set of non-linear ordinary differential equations.
We numerically find inhomogeneous compact Einstein spaces with orbifold
singularity.Comment: LaTeX 28 pages, 5 eps figure
Generalized Kahler manifolds and off-shell supersymmetry
We solve the long standing problem of finding an off-shell supersymmetric
formulation for a general N = (2, 2) nonlinear two dimensional sigma model.
Geometrically the problem is equivalent to proving the existence of special
coordinates; these correspond to particular superfields that allow for a
superspace description. We construct and explain the geometric significance of
the generalized Kahler potential for any generalized Kahler manifold; this
potential is the superspace Lagrangian.Comment: 21 pages; references clarified and added; theorem generalized; typos
correcte
Scalar--Flat Lorentzian Einstein--Weyl Spaces
We find all three-dimensional Einstein--Weyl spaces with the vanishing scalar
curvatureComment: 4 page
U-duality in three and four dimensions
Using generalised geometry we study the action of U-duality acting in three
and four dimensions on the bosonic fields of eleven dimensional supergravity.
We compare the U-duality symmetry with the T-duality symmetry of double field
theory and see how the and SL(5) U-duality groups reduce
to the SO(2,2) and SO(3,3) T-duality symmetry groups of the type IIA theory. As
examples we dualise M2-branes, both black and extreme. We find that uncharged
black M2-branes become charged under U-duality, generalising the Harrison
transformation, while extreme M2-branes will become new extreme M2-branes. The
resulting tension and charges are quantised appropriately if we use the
discrete U-duality group .Comment: v1: 35 pages; v2: minor corrections in section 4.1.2, many references
added; v3: further discussion added on the conformal factor of the
generalised metric in section 2 and on the Wick-rotation used to construct
examples in section
Membranes for Topological M-Theory
We formulate a theory of topological membranes on manifolds with G_2
holonomy. The BRST charges of the theories are the superspace Killing vectors
(the generators of global supersymmetry) on the background with reduced
holonomy G_2. In the absence of spinning formulations of supermembranes, the
starting point is an N=2 target space supersymmetric membrane in seven
euclidean dimensions. The reduction of the holonomy group implies a twisting of
the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations
in the normal bundle, in contrast to the ordinary spinning formulation of
topological strings, where twisting is performed with internal U(1) currents of
the N=(2,2) superconformal algebra. The double dimensional reduction on a
circle of the topological membrane gives the strings of the topological A-model
(a by-product of this reduction is a Green-Schwarz formulation of topological
strings). We conclude that the action is BRST-exact modulo topological terms
and fermionic equations of motion. We discuss the role of topological membranes
in topological M-theory and the relation of our work to recent work by Hitchin
and by Dijkgraaf et al.Comment: 22 pp, plain tex. v2: refs. adde
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