scholarly journals Toric Structures on the Moduli Space of Flat Connections on a Riemann Surface: Volumes and the Moment Map

1994 ◽  
Vol 106 (2) ◽  
pp. 151-168 ◽  
Author(s):  
L.C. Jeffrey ◽  
J. Weitsman
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Moment Map ◽  
Flat Connections ◽  
The Moment

Moduli Space of Flat Connections as a Poisson Manifold

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3195-3206 ◽  
Author(s):  
V. V. Fock ◽  
A. A. Rosly
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Poisson Structure ◽  
Moduli Space ◽  
Poisson Manifold ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Flat Connections ◽  
Lattice Gauge ◽  
Poisson Lie Groups

In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

scholarly journals A Note on Toric Varieties Associated with Moduli Spaces

2011 ◽  
Vol 54 (3) ◽  
pp. 561-565
Author(s):  
James J. Uren
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Toric Variety ◽  
Toric Varieties ◽  
Pants Decomposition ◽  
Basic Facts ◽  
The Moment ◽  
Moment Polytopes

AbstractIn this note we give a brief review of the construction of a toric variety coming from a genus g ≥ 2 Riemann surface Σg equipped with a trinion, or pair of pants, decomposition. This was outlined by J. Hurtubise and L. C. Jeffrey. A. Tyurin used this construction on a certain collection of trinion decomposed surfaces to produce a variety DMg , the so-called Delzant model of moduli space, for each genus g. We conclude this note with some basic facts about the moment polytopes of the varieties . In particular, we show that the varieties DMg constructed by Tyurin, and claimed to be smooth, are in fact singular for g ≥ 3.

Symplectic Geometry of the Moduli Space of Flat Connections on a Riemann Surface: Inductive Decompositions and Vanishing Theorems

2000 ◽  
Vol 52 (3) ◽  
pp. 582-612 ◽  
Author(s):  
Lisa C. Jeffrey ◽  
Jonathan Weitsman
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Chern Class ◽  
Boundary Component ◽  
Symplectic Geometry ◽  
Line Bundles ◽  
Vanishing Theorems ◽  
Stable Bundles ◽  
Flat Connections ◽  
First Chern Class

AbstractThis paper treats the moduli space g,1(Λ) of representations of the fundamental group of a Riemann surface of genus g with one boundary component which send the loop around the boundary to an element conjugate to exp Λ, where Λ is in the fundamental alcove of a Lie algebra. We construct natural line bundles over g,1(Λ) and exhibit natural homology cycles representing the Poincaré dual of the first Chern class. We use these cycles to prove differential equations satisfied by the symplectic volumes of these spaces. Finally we give a bound on the degree of a nonvanishing element of a particular subring of the cohomology of the moduli space of stable bundles of coprime rank k and degree d.

scholarly journals Half density quantization of the moduli space of flat connections and witten's semiclassical manifold invariants

Topology ◽  
1993 ◽  
Vol 32 (3) ◽  
pp. 509-529 ◽  
Author(s):  
Lisa C. Jeffrey ◽  
Jonathan Weitsman
Keyword(s):  
Moduli Space ◽  
Flat Connections

Kählerian potentials and convexity properties of the moment map

1996 ◽  
Vol 126 (1) ◽  
pp. 65-84 ◽  
Author(s):  
Peter Heinzner ◽  
Alan Huckleberry
Keyword(s):  
Moment Map ◽  
Convexity Properties ◽  
The Moment

scholarly journals Bootstrapping Coulomb and Higgs branch operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aleix Gimenez-Grau ◽  
Pedro Liendo
Keyword(s):  
Recent Work ◽  
Moment Map ◽  
Mixed System ◽  
Flavor Symmetry ◽  
Coulomb Branch ◽  
Conformal Bootstrap ◽  
General Constraints ◽  
Superconformal Theories ◽  
The Moment

Abstract We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in 4d$$ \mathcal{N} $$ N = 2 superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large r charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry.

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