scholarly journals Topological sectors and measures on moduli space in quantum Yang–Mills on a Riemann surface

1996 ◽  
Vol 37 (3) ◽  
pp. 1161-1170 ◽  
Author(s):  
Dana Stanley Fine
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Yang Mills

PARABOLIC VECTOR BUNDLES AND HERMITIAN-YANG-MILLS CONNECTIONS OVER A RIEMANN SURFACE

1993 ◽  
Vol 04 (03) ◽  
pp. 467-501 ◽  
Author(s):  
JONATHAN A. PORITZ
Keyword(s):  
Riemann Surface ◽  
Vector Bundle ◽  
Sobolev Space ◽  
Moduli Space ◽  
Vector Bundles ◽  
Weighted Sobolev Space ◽  
Conjugacy Classes ◽  
Stable Bundle ◽  
Yang Mills ◽  
Parabolic Bundles

We study a certain moduli space of irreducible Hermitian-Yang-Mills connections on a unitary vector bundle over a punctured Riemann surface. The connections used have non-trivial holonomy around the punctures lying in fixed conjugacy classes of U (n) and differ from each other by elements of a weighted Sobolev space; these connections give rise to parabolic bundles in the sense of Mehta and Seshadri. We show in fact that the moduli space of stable parabolic bundles can be identified with our moduli space of HYM connections, by proving that every stable bundle admits a unique unitary gauge orbit of Hermitian-Yang-Mills connections.

scholarly journals Moduli Spaces of Vector Bundles over a Real Curve: ℤ/2-Betti Numbers

2014 ◽  
Vol 66 (5) ◽  
pp. 961-992 ◽  
Author(s):  
Thomas Baird
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Lagrangian Submanifolds ◽  
Betti Numbers ◽  
Stable Bundles ◽  
Complex Curve ◽  
Yang Mills ◽  
Real Curve

AbstractModuli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi–stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah–Bott's “Yang–Mills over a Riemann Surface” to compute ℤ/2–Betti numbers of these spaces.

The Yang-Mills equations over Riemann surfaces

1983 ◽  
Vol 308 (1505) ◽  
pp. 523-615 ◽  
Keyword(s):  
Riemann Surface ◽  
Gauge Symmetry ◽  
Moduli Space ◽  
Morse Theory ◽  
Riemann Surfaces ◽  
Point Of View ◽  
Yang Mills ◽  
Critical Sets

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 ‘perfect' 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.

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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