The Moduli Space of Yang–Mills Connections Over a Compact Surface

1997 ◽  
Vol 09 (01) ◽  
pp. 77-121 ◽  
Author(s):  
Ambar Sengupta
Keyword(s):  
Explicit Formula ◽  
Moduli Space ◽  
Symplectic Structure ◽  
Compact Surface ◽  
Gauge Groups ◽  
Yang Mills

Yang–Mills connections over closed oriented surfaces of genus ≥1, for compact connected gauge groups, are constructed explicitly. The resulting formulas for Yang–Mills connections are used to carry out a Marsden–Weinstein type procedure. An explicit formula is obtained for the resulting 2-form on the moduli space. It is shown that this 2-form provides a symplectic structure on appropriate subsets of the moduli space.

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.

scholarly journals The moduli space and monodromies of the N = 2 supersymmetric Yang-Mills theory with any Lie gauge groups

1996 ◽  
Vol 480 (1-2) ◽  
pp. 279-295 ◽  
Author(s):  
M.R. Abolhasani ◽  
M. Alishahiha ◽  
A.M. Ghezelbash
Keyword(s):  
Moduli Space ◽  
Gauge Groups ◽  
Yang Mills

scholarly journals Large Deviations for the Yang-Mills Measure on a Compact Surface

2005 ◽  
Vol 261 (2) ◽  
pp. 405-450 ◽  
Author(s):  
Thierry Lévy ◽  
James R. Norris
Keyword(s):  
Large Deviations ◽  
Compact Surface ◽  
Yang Mills

scholarly journals Complex algebraic compactifications of the moduli space of Hermitian Yang–Mills connections on a projective manifold

2021 ◽  
Vol 25 (4) ◽  
pp. 1719-1818
Author(s):  
Daniel Greb ◽  
Benjamin Sibley ◽  
Matei Toma ◽  
Richard Wentworth
Keyword(s):  
Moduli Space ◽  
Projective Manifold ◽  
Yang Mills

scholarly journals Yang–Mills moduli space in the adiabatic limit

2015 ◽  
Vol 48 (42) ◽  
pp. 425401 ◽  
Author(s):  
Olaf Lechtenfeld ◽  
Alexander D Popov
Keyword(s):  
Moduli Space ◽  
Adiabatic Limit ◽  
Yang Mills
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