Elementary Properties of Moment Maps

2019 ◽  
pp. 21-26
Author(s):  
Shubham Dwivedi ◽  
Jonathan Herman ◽  
Lisa C. Jeffrey ◽  
Theo van den Hurk
Keyword(s):  
Moment Maps

scholarly journals 4d mirror-like dualities

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Chiung Hwang ◽  
Sara Pasquetti ◽  
Matteo Sacchi
Keyword(s):  
Dimensional Reduction ◽  
Moment Maps ◽  
Turn On ◽  
New Strategy ◽  
Real Mass ◽  
The Moment

Abstract We construct a family of 4d$$ \mathcal{N} $$ N = 1 theories that we call $$ {E}_{\rho}^{\sigma } $$ E ρ σ [USp(2N)] which exhibit a novel type of 4d IR duality very reminiscent of the mirror duality enjoyed by the 3d$$ \mathcal{N} $$ N = 4 $$ {T}_{\rho}^{\sigma } $$ T ρ σ [SU(N)] theories. We obtain the $$ {E}_{\rho}^{\sigma } $$ E ρ σ [USp(2N)] theories from the recently introduced E[USp(2N )] theory, by following the RG flow initiated by vevs labelled by partitions ρ and σ for two operators transforming in the antisymmetric representations of the USp(2N) × USp(2N) IR symmetries of the E[USp(2N)] theory. These vevs are the 4d uplift of the ones we turn on for the moment maps of T[SU(N)] to trigger the flow to $$ {T}_{\rho}^{\sigma } $$ T ρ σ [SU(N)]. Indeed the E[USp(2N)] theory, upon dimensional reduction and suitable real mass deformations, reduces to the T[SU(N)] theory. In order to study the RG flows triggered by the vevs we develop a new strategy based on the duality webs of the T[SU(N)] and E[USp(2N)] theories.

scholarly journals Equivariant indices of $\operatorname{Spin}^{c}$ -Dirac operators for proper moment maps

2017 ◽  
Vol 166 (6) ◽  
pp. 1125-1178 ◽  
Author(s):  
Peter Hochs ◽  
Yanli Song
Keyword(s):  
Dirac Operators ◽  
Moment Maps

Complex structures, moment maps, and the Ricci form

2020 ◽  
Vol 24 (5) ◽  
pp. 821-854
Author(s):  
Oscar García-Prada ◽  
Dietmar A. Salamon ◽  
Samuel Trautwein
Keyword(s):  
Complex Structures ◽  
Moment Maps ◽  
Ricci Form

scholarly journals Geometric quantization for proper moment maps

2009 ◽  
Vol 347 (7-8) ◽  
pp. 389-394 ◽  
Author(s):  
Xiaonan Ma ◽  
Weiping Zhang
Keyword(s):  
Geometric Quantization ◽  
Moment Maps

Abstract moment maps

2002 ◽  
pp. 31-43
Author(s):  
Victor Guillemin ◽  
Viktor Ginzburg ◽  
Yael Karshon
Keyword(s):  
Moment Maps

scholarly journals Searching for kinematic evidence of Keplerian disks around Class 0 protostars with CALYPSO

2020 ◽  
Vol 635 ◽  
pp. A15 ◽  
Author(s):  
S. Maret ◽  
A. J. Maury ◽  
A. Belloche ◽  
M. Gaudel ◽  
Ph. André ◽  
...  
Keyword(s):  
Optical Thickness ◽  
Angular Resolution ◽  
Line Emission ◽  
Protoplanetary Disks ◽  
High Angular Resolution ◽  
Moment Maps ◽  
Large Program ◽  
Jet Axis

The formation of protoplanetary disks is not well understood. To understand how and when these disks are formed, it is crucial to characterize the kinematics of the youngest protostars at a high angular resolution. Here we study a sample of 16 Class 0 protostars to measure their rotation profile at scales from 50 to 500 au and search for Keplerian rotation. We used high-angular-resolution line observations obtained with the Plateau de Bure Interferometer as part of the CALYPSO large program. From 13CO (J = 2−1), C18O (J = 2−1) and SO (Nj = 56−45) moment maps, we find that seven sources show rotation about the jet axis at a few hundred au scales: SerpS-MM18, L1448-C, L1448-NB, L1527, NGC 1333-IRAS 2A, NGC 1333-IRAS 4B, and SVS13-B. We analyzed the kinematics of these sources in the uv plane to derive the rotation profiles down to 50 au scales. We find evidence for Keplerian rotation in only two sources, L1527 and L1448-C. Overall, this suggests that Keplerian disks larger than 50 au are uncommon around Class 0 protostars. However, in some of the sources, the line emission could be optically thick and dominated by the envelope emission. Due to the optical thickness of these envelopes, some of the disks could have remained undetected in our observations.

scholarly journals Geometric quantization for proper moment maps: the Vergne conjecture

2014 ◽  
Vol 212 (1) ◽  
pp. 11-57 ◽  
Author(s):  
Xiaonan Ma ◽  
Weiping Zhang
Keyword(s):  
Geometric Quantization ◽  
Moment Maps
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