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

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

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.

SINGULARITY STRUCTURE OF ${\mathcal N} = 2$ SUPERSYMMETRIC YANG–MILLS THEORIES

2013 ◽  
Vol 28 (20) ◽  
pp. 1330029 ◽  
Author(s):  
JIHYE SOFIA SEO
Keyword(s):  
Moduli Space ◽  
Riemann Surfaces ◽  
Magnetic Monopoles ◽  
Gauge Groups ◽  
Singularity Structure ◽  
Yang Mills ◽  
Geometric Singularity ◽  
Physical Singularity ◽  
Monopoles And Dyons ◽  
Nontrivial Topology

In this paper, we consider the case where electrons, magnetic monopoles and dyons become massless. Here, we consider the [Formula: see text] supersymmetric Yang–Mills (SYM) theories with classical gauge groups with a rank r, SU(r+1), SO(2r), Sp(2r) and SO(2r+1) which are studied by Riemann surfaces called Seiberg–Witten curves. We discuss physical singularity associated with massless particles, which can be studied by geometric singularity of vanishing 1-cycles in Riemann surfaces in hyperelliptic form. We pay particular attention to the cases where mutually nonlocal states become massless (Argyres–Douglas theories), which corresponds to Riemann surfaces degenerating into cusps. We discuss nontrivial topology on the moduli space of the theory, which is reflected as monodromy associated to vanishing 1-cycles. We observe how dyon charges get changed as we move around and through singularity in moduli space.

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