966 research outputs found
String-Like Lagrangians from a Generalized Geometry
This note will use Hitchin's generalized geometry and a model of axionic
gravity developed by Warren Siegel in the mid-nineties to show that the
construction of Lagrangians based on the inner product arising from the pairing
of a vector and its dual can lead naturally to the low-energy Lagrangian of the
bosonic string.Comment: Conclusions basically unchanged, but presentation streamlined
significantly. Published versio
Double solid twistor spaces: the case of arbitrary signature
In a recent paper (math.DG/0701278) we constructed a series of new Moishezon
twistor spaces which is a kind of variant of the famous LeBrun twistor spaces.
In this paper we explicitly give projective models of another series of
Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a
generalization of the twistor spaces of a 'double solid type' on 3CP^2 studied
by Kreussler, Kurke, Poon and the author. Similarly to the twistor spaces of
'double solid type' on 3CP^2, projective models of present twistor spaces have
a natural structure of double covering of a CP^2-bundle over CP^1. We
explicitly give a defining polynomial of the branch divisor of the double
covering whose restriction to fibers are degree four. If n>3 these are new
twistor spaces, to the best of the author's knowledge. We also compute the
dimension of the moduli space of these twistor spaces. Differently from
math.DG/0701278, the present investigation is based on analysis of
pluri-(half-)anticanonical systems of the twistor spaces.Comment: 30 pages, 3 figures; v2: title changed (the original title was
"Explicit construction of new Moishezon twistor spaces, II".
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
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
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
Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds
The precise relation between Kodaira-Spencer path integral and a particular
wave function in seven dimensional quadratic field theory is established. The
special properties of three-forms in 6d, as well as Hitchin's action
functional, play an important role. The latter defines a quantum field theory
similar to Polyakov's formulation of 2d gravity; the curious analogy with
world-sheet action of bosonic string is also pointed out.Comment: 31 page
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
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
Geometry for the accelerating universe
The Lorentzian spacetime metric is replaced by an area metric which naturally
emerges as a generalized geometry in quantum string and gauge theory. Employing
the area metric curvature scalar, the gravitational Einstein-Hilbert action is
re-interpreted as dynamics for an area metric. Without the need for dark energy
or fine-tuning, area metric cosmology explains the observed small acceleration
of the late Universe.Comment: 4 pages, 1 figur
Interacting Strings in Matrix String Theory
It is here explained how the Green-Schwarz superstring theory arises from
Matrix String Theory. This is obtained as the strong YM-coupling limit of the
theory expanded around its BPS instantonic configurations, via the
identification of the interacting string diagram with the spectral curve of the
relevant configuration. Both the GS action and the perturbative weight
, where is the Euler characteristic of the world-sheet
surface and the string coupling, are obtained.Comment: 11 pages, no figures, two references adde
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