scholarly journals Renormalisation flow and geodesics on the moduli space of four dimensional N=2 supersymmetric Yang–Mills theory

1998 ◽  
Vol 418 (1-2) ◽  
pp. 107-110 ◽  
Author(s):  
Brian P. Dolan
Keyword(s):  
Moduli Space ◽  
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

Holonomies of Yang–Mills connections for bundles on a surface with disconnected structure group

1994 ◽  
Vol 116 (2) ◽  
pp. 375-384 ◽  
Author(s):  
Johannes Huebschmann
Keyword(s):  
Moduli Space ◽  
Scalar Product ◽  
Additive Group ◽  
Closed Surface ◽  
Riemannian Metric ◽  
Compact Lie Group ◽  
Universal Central Extension ◽  
Yang Mills ◽  
Disconnected Structure ◽  
Image Position

AbstractLet Σ be a closed surface of genus ≥ 1, G a compact Lie group, not necessarily connected with Lie algebra g, ξ,: P → Σ a principal G-bundle, and suppose Σ equipped with a Riemannian metric and g with an invariant scalar product so that the Yang—Mills equations on ξ are defined. Further, letbe the universal central extension of the fundamental group π of Σ and ΓR the group obtained from Γ when its centre Z is extended to the additive group R of the reals. We show that there are bijective correspondences between various spaces of classes of Yang—Mills connections on ξ and spaces of representations of Γ and ΓR (as appropriate) in G. In particular, we show that the holonomy establishes a homeomorphism between the moduli space N(ξ) of central Yang–Mills connections on ξ and the space Repξ(Γ, G) of representations of Γ in G determined by ξ. Our results rely on a detailed study of the holonomy of a central Yang–Mills connection and extend corresponding ones of Atiyah and Bott for the case where G is connected.

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.

scholarly journals The geometry of the Yang-Mills moduli space for definite manifolds

1989 ◽  
Vol 29 (3) ◽  
pp. 499-544 ◽  
Author(s):  
David Groisser ◽  
Thomas H. Parker
Keyword(s):  
Moduli Space ◽  
Yang Mills

scholarly journals 4d Chern-Simons theory as a 3d Toda theory, and a 3d-2d correspondence

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Meer Ashwinkumar ◽  
Kee-Seng Png ◽  
Meng-Chwan Tan
Keyword(s):  
Moduli Space ◽  
Sigma Model ◽  
Three Dimensional ◽  
Simons Theory ◽  
Yang Mills ◽  
Pole Type ◽  
Type Boundary ◽  
Chern Simons ◽  
Manifold With Corners ◽  
Chern Simons Theory

Abstract We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations. This furnishes a novel 3d-2d correspondence, which, among other mathematical implications, also reveals that modules of the 3d W-algebra are modules for the quantized algebra of certain holomorphic functions on the Bogomolny moduli space.

scholarly journals Higgs Branch, Hyper-Kähler Quotient and Duality in SUSY N = 2 Yang–Mills Theories

1997 ◽  
Vol 12 (27) ◽  
pp. 4907-4931 ◽  
Author(s):  
I. Antoniadis ◽  
B. Pioline
Keyword(s):  
Moduli Space ◽  
Gauge Theories ◽  
Geometric Interpretation ◽  
Low Energy ◽  
Target Space ◽  
Field Theories ◽  
Yang Mills ◽  
Coulomb Phase ◽  
Supersymmetric Field Theories ◽  
Energy Theory

Low-energy limits of N = 2 supersymmetric field theories in the Higgs branch are described in terms of a nonlinear four-dimensional σ-model on a hyper-Kähler target space, classically obtained as a hyper-Kähler quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low-energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg–Witten SU(2) theory with Nf flavors, interpreted by Witten as a small instanton singularity in the moduli space of one instanton on ℝ4. By explicitly evaluating the metric, we show that this Higgs branch coincides with the Higgs branch of a U(1) N = 2 SUSY theory with the number of flavors predicted by the singularity structure of Seiberg–Witten's theory in the Coulomb phase. We find another example of Higgs phase duality, namely between the Higgs phases of U(Nc)Nf flavors and U(Nf-Nc)Nf flavors theories, by using a geometric interpretation due to Biquard et al. This duality may be relevant for understanding Seiberg's conjectured duality Nc ↔ Nf-Nc in N = 1 SUSY SU(Nc) gauge theories.

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