Journal ArticleDOI
The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
Reads0
Chats0
TLDR
In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.Abstract:
The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect9 functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail.read more
Citations
More filters
Journal ArticleDOI
About $G$-bundles over elliptic curves
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/legal.php) of a fichier do not necessarily imply a mention of copyright.
Posted Content
A New Look At The Path Integral Of Quantum Mechanics
TL;DR: In this paper, it was shown that possible integration cycles for the Feynman path integral of ordinary quantum mechanics are associated with branes in a two-dimensional A-model.
Journal ArticleDOI
Exceptional Calabi–Yau spaces: the geometry of N=2 backgrounds with flux
Anthony Ashmore,Daniel Waldram +1 more
TL;DR: In this paper, the authors define the analogue of Calabi-Yau geometry for generic D=4, N=2 flux backgrounds in type II supergravity and M-theory, and show that solutions of the Killing spinor equations are in one-toone correspondence with integrable, globally defined structures in E7(7)×R+ generalised geometry.
Book ChapterDOI
Analogies between the Langlands Correspondence and Topological Quantum Field Theory
TL;DR: In this article, a rough conjectural framework for the Langlands theory for higher-dimensional schemes is presented, which can be used to formulate a more detailed program for higher dimensional Galois groups.
Journal ArticleDOI
From Black Holes to Quivers
TL;DR: In this paper, a general algorithm for reconstructing the full moduli-dependent cohomology of the moduli space of an arbitrary quiver, in terms of the BPS invariants of the pure Higgs states, was proposed.
References
More filters
Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
Book
Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
Book
Geometric Invariant Theory
TL;DR: Geometric invariant theory for moduli spaces has been studied extensively in the mathematical community as mentioned in this paper, with a large number of applications to the moduli space construction problem, see, for instance, the work of Mumford and Fogarty.
Journal ArticleDOI
Self-duality in four-dimensional Riemannian geometry
TL;DR: In this article, the authors present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis, and apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group.
Journal ArticleDOI
Stable and unitary vector bundles on a compact Riemann surface
M. S. Narasimhan,C. S. Seshadri +1 more
TL;DR: In this article, it was shown that on the space of isomorphic classes of unitary vector bundles on X of a given rank, there is a natural structure of a normal projective variety (Theorem 8.1).