The Yang-Mills Equations over Riemann Surfaces

1995 ◽  
pp. 148-240 ◽  
Author(s):  
M. F. Atiyah ◽  
R. Bott
Keyword(s):  
Riemann Surfaces ◽  
Yang Mills

scholarly journals Non-supersymmetric matrix strings from generalized Yang–Mills theory on arbitrary Riemann surfaces

2000 ◽  
Vol 576 (1-3) ◽  
pp. 241-264 ◽  
Author(s):  
M. Billó ◽  
A. D'Adda ◽  
P. Provero
Keyword(s):  
Riemann Surfaces ◽  
Yang Mills

Yang?Mills instantons over Riemann surfaces

1992 ◽  
Vol 24 (4) ◽  
pp. 275-281 ◽  
Author(s):  
M. Lled� ◽  
I. Mart�n ◽  
A. Restuccia ◽  
A. Mendoza
Keyword(s):  
Riemann Surfaces ◽  
Yang Mills

MODULI OF STABLE PAIRS FOR HOLOMORPHIC BUNDLES OVER RIEMANN SURFACES

1991 ◽  
Vol 02 (05) ◽  
pp. 477-513 ◽  
Author(s):  
STEVEN B. BRADLOW ◽  
GEORGIOS D. DASKALOPOULOS
Keyword(s):  
Moduli Space ◽  
Riemann Surfaces ◽  
Holomorphic Section ◽  
Stable Bundles ◽  
Space Problem ◽  
Yang Mills ◽  
Closed Riemann Surface ◽  
Holomorphic Bundles ◽  
Stable Pairs ◽  
Compact Kähler Manifold

It this paper we study the space of gauge equivalence classes of pairs [Formula: see text] where [Formula: see text] represents a holomorphic structure on a complex bundle, E, over a closed Riemann Surface, and ϕ is a holomorphic section. We define a space of stable pairs and consider the moduli space problem for this space. The space of stable pairs, [Formula: see text], is related to the space of solution to the Vortex (Hermitian-Yang-Mills-Higgs) equation. Using the parameter, τ, which appears in this equation we can define subspaces [Formula: see text] within [Formula: see text]. We show that under suitable restrictions on τ and the degree of E, the space [Formula: see text] is naturally a finite dimensional, Hausdorff, compact Kähler manifold. We show further that there is a natural holomorphic map from this space onto the Seshadri compactification of the moduli space of stable bundles and that this map is generically a fibration.

scholarly journals QCD INSTANTONS AND 2D SURFACES

1992 ◽  
Vol 07 (11) ◽  
pp. 1001-1008 ◽  
Author(s):  
V.G.J. RODGERS
Keyword(s):  
Riemann Surface ◽  
Axial Symmetry ◽  
Riemann Surfaces ◽  
Coadjoint Orbits ◽  
Holomorphic Maps ◽  
Topological Information ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Relationship ◽  
Effective Description

Some time ago, Atiyah showed that there exists a natural identification between the k-instantons of a Yang-Mills theory with gauge group G and the holomorphic maps from CP1 to ΩG. Since then, Nair and Mazur have associated the Θ vacua structure in QCD with self-intersecting Riemann surfaces immersed in four dimensions. From here they concluded that these 2D surfaces correspond to the non-perturbative phase of QCD and carry the topological information of the Θ vacua. In this paper we would like to elaborate on this point by making use of Atiyah’s identification. We will argue that an effective description of QCD may be more like a WZW model coupled to the induced metric of an immersion of a 2D Riemann surface in R4. We make some further comments on the relationship between the coadjoint orbits of the Kac-Moody group on G and instantons with axial symmetry and monopole charge.

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