Critical points for the square of the moment map

2020 ◽  
pp. 35-43
Keyword(s):  
Critical Points ◽  
Moment Map ◽  
The Moment

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.

scholarly journals Brick Manifolds and Toric Varieties of Brick Polytopes

10.37236/5038 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Laura Escobar
Keyword(s):  
Toric Variety ◽  
Toric Varieties ◽  
Moment Map ◽  
Twisted Product ◽  
General Fiber ◽  
Moment Polytope ◽  
The Moment ◽  
Subword Complex ◽  
Do So

Bott-Samelson varieties are a twisted product of $\mathbb{C}\mathbb{P}^1$'s with a map into $G/B$. These varieties are mostly studied in the case in which the map into $G/B$ is birational to the image; however in this paper we study a fiber of this map when it is not birational. We prove that in some cases the general fiber, which we christen a brick manifold, is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to translate this problem into one in terms of the "subword complexes" of Knutson and Miller. Pilaud and Stump realized certain subword complexes as the dual of the boundary of a polytope which generalizes the brick polytope defined by Pilaud and Santos. For a nice family of words, the brick polytope is the generalized associahedron realized by Hohlweg, Lange and Thomas. These stories connect in a nice way: we show that the moment polytope of the brick manifold is the brick polytope. In particular, we give a nice description of the toric variety of the associahedron. We give each brick manifold a stratification dual to the subword complex. In addition, we relate brick manifolds to Brion's resolutions of Richardon varieties.

The moment map

1994 ◽  
pp. 144-189
Author(s):  
David Mumford ◽  
John Fogarty ◽  
Frances Kirwan
Keyword(s):  
Moment Map ◽  
The Moment
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