781 research outputs found
Goto's generalized Kaehler stability theorem
In these notes we give a shortened and more direct proof of Goto's
generalized Kaehler stability theorem stating that if (J_1,J_2) is a
generalized kaehler structure for which J_2 is determined by a nowhere
vanishing closed form, then small deformations of J_1 can be coupled with small
deformations of J_2 so that the pair remains a generalized Kaehler structure.Comment: 9 pages, 5 figure
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
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
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,
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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
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
Geometric transitions and integrable systems
We consider {\bf B}-model large duality for a new class of noncompact
Calabi-Yau spaces modeled on the neighborhood of a ruled surface in a
Calabi-Yau threefold. The closed string side of the transition is governed at
genus zero by an Hitchin integrable system on a genus Riemann surface
. The open string side is described by a holomorphic Chern-Simons
theory which reduces to a generalized matrix model in which the eigenvalues lie
on the compact Riemann surface . We show that the large planar
limit of the generalized matrix model is governed by the same Hitchin
system therefore proving genus zero large duality for this class of
transitions.Comment: 70 pages, 1 figure; version two: minor change
On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds
We derive the complete supergravity description of the N=2 scalar potential
which realizes a generic flux-compactification on a Calabi-Yau manifold
(generalized geometry). The effective potential V_{eff}=V_{(\partial_Z V=0)},
obtained by integrating out the massive axionic fields of the special
quaternionic manifold, is manifestly mirror symmetric, i.e. invariant with
respect to {\rm Sp}(2 h_2+2)\times {\rm Sp}(2 h_1+2) and their exchange, being
h_1, h_2 the complex dimensions of the underlying special geometries. {\Scr
V}_{eff} has a manifestly N=1 form in terms of a mirror symmetric
superpotential W$ proposed, some time ago, by Berglund and Mayr.Comment: 14 pages, LaTeX sourc
Blowing up generalized Kahler 4-manifolds
We show that the blow-up of a generalized Kahler 4-manifold in a
nondegenerate complex point admits a generalized Kahler metric. As with the
blow-up of complex surfaces, this metric may be chosen to coincide with the
original outside a tubular neighbourhood of the exceptional divisor. To
accomplish this, we develop a blow-up operation for bi-Hermitian manifolds.Comment: 16 page
Scalar--Flat Lorentzian Einstein--Weyl Spaces
We find all three-dimensional Einstein--Weyl spaces with the vanishing scalar
curvatureComment: 4 page
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