Cauchy-Riemann Operators, Self-Duality, and the Spectral Flow

1994 ◽  
pp. 511-545
Author(s):  
Stamatis Dostoglou ◽  
Dietmar A. Salamon
Keyword(s):  
Spectral Flow ◽  
Self Duality ◽  
Cauchy Riemann

Cauchy-Riemann Operators, Self—Duality, and the Spectral Flow

1994 ◽  
pp. 511-545 ◽  
Author(s):  
Stamatis Dostoglou ◽  
Dietmar A. Salamon
Keyword(s):  
Spectral Flow ◽  
Self Duality ◽  
Cauchy Riemann

SOME BOUNDARY VALUE PROBLEMS FOR THE CAUCHY-RIEMANN EQUATION IN HALF LENS

2018 ◽  
Vol 9 (3) ◽  
pp. 73-84
Author(s):  
N. Taghizadeh ◽  
◽  
V. Soltani Mohammadi ◽  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Riemann Equation ◽  
Cauchy Riemann

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

Invariance of projective modules in $$\mathsf {Sup}$$ under self-duality

2021 ◽  
Vol 82 (1) ◽  
Author(s):  
Javier Gutiérrez García ◽  
Ulrich Höhle ◽  
Tomasz Kubiak
Keyword(s):  
Projective Modules ◽  
Self Duality

scholarly journals Potential and challenges of wind measurements using met-masts in complex topography for bridge design: Part II – Spectral flow characteristics

2021 ◽  
Vol 211 ◽  
pp. 104585
Author(s):  
Zakari Midjiyawa ◽  
Etienne Cheynet ◽  
Joachim Reuder ◽  
Hálfdán Ágústsson ◽  
Trond Kvamsdal
Keyword(s):  
Flow Characteristics ◽  
Spectral Flow ◽  
Complex Topography ◽  
Bridge Design ◽  
Wind Measurements

scholarly journals Condensation of SIP Particles and Sticky Brownian Motion

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Mario Ayala ◽  
Gioia Carinci ◽  
Frank Redig
Keyword(s):  
Brownian Motion ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Self Duality ◽  
Inclusion Process ◽  
Interacting Particle ◽  
New Information ◽  
Homogeneous Product ◽  
Coarsening Dynamics ◽  
The Difference

AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.

scholarly journals Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri
Keyword(s):  
Vector Field ◽  
Extended Supersymmetry ◽  
General Framework ◽  
Gauge Theories ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Explicit Result ◽  
Yang Mills ◽  
Self Duality ◽  
Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

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