543 research outputs found
Matrix String Theory and its Moduli Space
The correspondence between Matrix String Theory in the strong coupling limit
and IIA superstring theory can be shown by means of the instanton solutions of
the former. We construct the general instanton solutions of Matrix String
Theory which interpolate between given initial and final string configurations.
Each instanton is characterized by a Riemann surface of genus h with n
punctures, which is realized as a plane curve. We study the moduli space of
such plane curves and find out that, at finite N, it is a discretized version
of the moduli space of Riemann surfaces: instead of 3h-3+n its complex
dimensions are 2h-3+n, the remaining h dimensions being discrete. It turns out
that as tends to infinity, these discrete dimensions become continuous, and
one recovers the full moduli space of string interaction theory.Comment: 30 pages, LaTeX, JHEP.cls class file, minor correction
String Interactions from Matrix String Theory
The Matrix String Theory, i.e. the two dimensional U(N) SYM with N=(8,8)
supersymmetry, has classical BPS solutions that interpolate between an initial
and a final string configuration via a bordered Riemann surface. The Matrix
String Theory amplitudes around such a classical BPS background, in the strong
Yang--Mills coupling, are therefore candidates to be interpreted in a stringy
way as the transition amplitude between given initial and final string
configurations. In this paper we calculate these amplitudes and show that the
leading contribution is proportional to the factor g_s^{-\chi}, where \chi is
the Euler characteristic of the interpolating Riemann surface and g_s is the
string coupling. This is the factor one expects from perturbative string
interaction theory.Comment: 15 pages, 2 eps figures, JHEP Latex class, misprints correcte
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
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
Automorphisms of moduli spaces of vector bundles over a curve
Let X be an irreducible smooth complex projective curve of genus g at least
4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank
r and fixed determinant \Lambda, of degree d. We give a new proof of the fact
that the automorphism group of M(r,\Lambda) is generated by automorphisms of
the curve X, tensorization with suitable line bundles, and, if r divides 2d,
also dualization of vector bundles.Comment: 12 page
Einstein-Hermitian connection on twisted Higgs bundles
Let be a smooth projective variety over . We prove that a
twisted Higgs vector bundle (\calE\, ,\theta) on admits an
Einstein--Hermitian connection if and only if (\calE\, ,\theta) is
polystable. A similar result for twisted vector bundles (no Higgs fields) was
proved by S. Wang in \cite{Wa}. Our approach is simpler.Comment: To appear in Comptes rendus Mathematiqu
Solitons and admissible families of rational curves in twistor spaces
It is well known that twistor constructions can be used to analyse and to
obtain solutions to a wide class of integrable systems. In this article we
express the standard twistor constructions in terms of the concept of an
admissible family of rational curves in certain twistor spaces. Examples of of
such families can be obtained as subfamilies of a simple family of rational
curves using standard operations of algebraic geometry. By examination of
several examples, we give evidence that this construction is the basis of the
construction of many of the most important solitonic and algebraic solutions to
various integrable differential equations of mathematical physics. This is
presented as evidence for a principal that, in some sense, all soliton-like
solutions should be constructable in this way.Comment: 15 pages, Abstract and introduction rewritten to clarify the
objectives of the paper. This is the final version which will appear in
Nonlinearit
BRST, anti-BRST and their geometry
We continue the comparison between the field theoretical and geometrical
approaches to the gauge field theories of various types, by deriving their
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST trasformation properties and
comparing them with the geometrical properties of the bundles and gerbes. In
particular, we provide the geometrical interpretation of the so--called
Curci-Ferrari conditions that are invoked for the absolute anticommutativity of
the BRST and anti-BRST symmetry transformations in the context of non-Abelian
1-form gauge theories as well as Abelian gauge theory that incorporates a
2-form gauge field. We also carry out the explicit construction of the 3-form
gauge fields and compare it with the geometry of 2--gerbes.Comment: A comment added. To appear in Jour. Phys. A: Mathemaical and
Theoretica
Generalized Kahler geometry and gerbes
We introduce and study the notion of a biholomorphic gerbe with connection.
The biholomorphic gerbe provides a natural geometrical framework for
generalized Kahler geometry in a manner analogous to the way a holomorphic line
bundle is related to Kahler geometry. The relation between the gerbe and the
generalized Kahler potential is discussed.Comment: 28 page
Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles
In this paper we give some examples of almost para-hyperhermitian structures
on the tangent bundle of an almost product manifold, on the product manifold
, where is a manifold endowed with a mixed 3-structure
and on the circle bundle over a manifold with a mixed 3-structure.Comment: 10 pages; This paper has been presented in the "4th German-Romanian
Seminar on Geometry" Dortmund, Germany, 15-18 July 200
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