Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 Definition and Properties of the GFF
- 2 Liouville Measure
- 3 Gaussian Multiplicative Chaos
- 4 Statistical Physics on Random Planar Maps
- 5 Introduction to Liouville Conformal Field Theory
- 6 Gaussian Free Field with Neumann Boundary Conditions
- 7 QuantumWedges and Scale-Invariant Random Surfaces
- 8 SLE and the Quantum Zipper
- 9 Liouville Quantum Gravity as a Mating of Trees
- Appendix A Chordal Loewner Chains and Chordal SLE
- Appendix B Reverse Loewner Flow and Reverse SLE
- Appendix C Radial Loewner Chains and Radial SLE
- Appendix D Convergence of Random Variables in the Space of Distributions
- References
- Notation and Symbols
- Index
7 - QuantumWedges and Scale-Invariant Random Surfaces
Published online by Cambridge University Press: 20 November 2025
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 Definition and Properties of the GFF
- 2 Liouville Measure
- 3 Gaussian Multiplicative Chaos
- 4 Statistical Physics on Random Planar Maps
- 5 Introduction to Liouville Conformal Field Theory
- 6 Gaussian Free Field with Neumann Boundary Conditions
- 7 QuantumWedges and Scale-Invariant Random Surfaces
- 8 SLE and the Quantum Zipper
- 9 Liouville Quantum Gravity as a Mating of Trees
- Appendix A Chordal Loewner Chains and Chordal SLE
- Appendix B Reverse Loewner Flow and Reverse SLE
- Appendix C Radial Loewner Chains and Radial SLE
- Appendix D Convergence of Random Variables in the Space of Distributions
- References
- Notation and Symbols
- Index
Summary
This chapter is devoted to the study of so-called quantum surfaces, which are fields defined on a parameterising domain, viewed up to an equivalence relation corresponding to the conformal change of coordinates formula of Chapter 2. We construct various special quantum surfaces enjoying scale-invariance properties, including quantum spheres, discs, wedges and cones. These objects are the conjectured scaling limits of families of random planar maps, as in Chapter 4 for example, depending on the imposed discrete topology. We conclude the chapter by explaining how these quantum surfaces are related in a rigorous way to the Liouville conformal field theory developed in Chapter 5.
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- Gaussian Free Field and Liouville Quantum Gravity , pp. 256 - 298Publisher: Cambridge University PressPrint publication year: 2025
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