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

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

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

scholarly journals Topological field theories on manifolds with Wu structures

2017 ◽  
Vol 29 (05) ◽  
pp. 1750015 ◽  
Author(s):  
Samuel Monnier
Keyword(s):  
Topological Field Theories ◽  
Geometric Quantization ◽  
Discrete Symmetry ◽  
Local System ◽  
Field Theories ◽  
Simons Theory ◽  
General Point ◽  
Topological Field ◽  
Generalized Cohomology ◽  
Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

Remarks on the geometric quantization of the Kepler problem

1988 ◽  
Vol 16 (3) ◽  
pp. 189-197 ◽  
Author(s):  
Giuseppe Gaeta ◽  
Mauro Spera
Keyword(s):  
Kepler Problem ◽  
Geometric Quantization

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
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