Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- Part II Solitons and Topology; Non-Abelian Theory
- Part III Other Spins or Statistics; General Relativity
- 33 Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics
- 34 Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General
- 35 Particle–Vortex Duality in Three Dimensions, Particle–String Duality in Four Dimensions, and p-Form Fields in Four Dimensions
- 36 Fermions and Dirac Spinors
- 37 The Dirac Equation and Its Solutions
- 38 General Relativity: Metric and General Coordinate Invariance
- 39 The Einstein Action and the Einstein Equation
- 40 Perturbative Gravity: Fierz-Pauli Action, de Donder Gauge and Other Gauges, Gravitational Waves
- 41 Nonperturbative Gravity: The Vacuum Schwarzschild Solution
- 42 Deflection of Light by the Sun and Comparison with General Relativity
- 43 Fully Linear Gravity: Parallel Plane (pp) Waves and Gravitational Shock Wave Solutions
- 44 Dimensional Reduction: The Domain Wall, Cosmic String, and BTZ Black Hole Solutions
- 45 Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution
- 46 Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons
- References
- Index
35 - Particle–Vortex Duality in Three Dimensions, Particle–String Duality in Four Dimensions, and p-Form Fields in Four Dimensions
from Part III - Other Spins or Statistics; General Relativity
Published online by Cambridge University Press: 04 March 2019
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- Part II Solitons and Topology; Non-Abelian Theory
- Part III Other Spins or Statistics; General Relativity
- 33 Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics
- 34 Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General
- 35 Particle–Vortex Duality in Three Dimensions, Particle–String Duality in Four Dimensions, and p-Form Fields in Four Dimensions
- 36 Fermions and Dirac Spinors
- 37 The Dirac Equation and Its Solutions
- 38 General Relativity: Metric and General Coordinate Invariance
- 39 The Einstein Action and the Einstein Equation
- 40 Perturbative Gravity: Fierz-Pauli Action, de Donder Gauge and Other Gauges, Gravitational Waves
- 41 Nonperturbative Gravity: The Vacuum Schwarzschild Solution
- 42 Deflection of Light by the Sun and Comparison with General Relativity
- 43 Fully Linear Gravity: Parallel Plane (pp) Waves and Gravitational Shock Wave Solutions
- 44 Dimensional Reduction: The Domain Wall, Cosmic String, and BTZ Black Hole Solutions
- 45 Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution
- 46 Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons
- References
- Index
Summary
We study dualities in various dimensions. We start with the example of Maxwell duality in 3+1 dimensions from the point of view of a transformation with a master action. We continue with the particle–vortex duality in 2+1 dimensions, also through a master action, and then the particle–string duality in 3+1 dimensions. Finally, we describe the general Poincaré duality in d dimensions, and we end with applications in 3+1 dimensions.
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- Information
- Classical Field Theory , pp. 330 - 337Publisher: Cambridge University PressPrint publication year: 2019