Basis for solutions of the Benoit & Saint-Aubin PDEs with particular asymptotics properties

Eveliina Peltola

doi:10.4171/AIHPD/81

Basis for solutions of the Benoit & Saint-Aubin PDEs with particular asymptotics properties

Eveliina Peltola^*

^*Corresponding author for this work

Not published at Aalto University

University of Geneva

Research output: Contribution to journal › Article › Scientific › peer-review

4 Citations (Scopus)

Abstract

Applying the quantum group method developed in [50], we construct solutions to the Benoit & Saint-Aubin partial differential equations with boundary conditions given by specific recursive asymptotics properties. Our results generalize solutions constructed in [49, 55], known as the pure partition functions of multiple Schramm-Loewner evolutions. The generalization is reminiscent of fusion in conformal field theory, and our solutions can be thought of as partition functions of systems of random curves, where many curves may emerge from the same point.

Original language	English
Pages (from-to)	1-73
Number of pages	73
Journal	Annales de l'Institut Henri Poincare D: Combinatorics, Physics and their Interactions
Volume	7
Issue number	1
DOIs	https://doi.org/10.4171/AIHPD/81
Publication status	Published - 2020
MoE publication type	A1 Journal article-refereed

Funding

Acknowledgments. During this work, the author was supported by Vilho, Yrjö and Kalle Väisälä Foundation and affiliated with the University of Helsinki. She wishes to especially thank Steven Flores and Kalle Kytölä for many inspiring discussions and ideas. She has also enjoyed stimulating and helpful discussions with Michel Bauer, Dmitry Chelkak, Julien Dubédat, Bertrand Duplantier, Philippe Di Francesco, Clément Hongler, Konstantin Izyurov, Jesper Jacobsen, Fredrik Johansson-Viklund, Rinat Kedem, Antti Kemppainen, Jonatan Lenells, Jason Miller, Wei Qian, Hubert Saleur, and Hao Wu. She thanks Roland Friedrich for pointing out important references.

Keywords

BPZ partial differential equations
Conformal field theory (CFT)
Loewner evolution (SLE)
Quantum group
Schramm

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10.4171/AIHPD/81

Cite this

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title = "Basis for solutions of the Benoit \& Saint-Aubin PDEs with particular asymptotics properties",

abstract = "Applying the quantum group method developed in [50], we construct solutions to the Benoit \& Saint-Aubin partial differential equations with boundary conditions given by specific recursive asymptotics properties. Our results generalize solutions constructed in [49, 55], known as the pure partition functions of multiple Schramm-Loewner evolutions. The generalization is reminiscent of fusion in conformal field theory, and our solutions can be thought of as partition functions of systems of random curves, where many curves may emerge from the same point.",

keywords = "BPZ partial differential equations, Conformal field theory (CFT), Loewner evolution (SLE), Quantum group, Schramm",

author = "Eveliina Peltola",

note = "Funding Information: Acknowledgments. During this work, the author was supported by Vilho, Yrj{\"o} and Kalle V{\"a}is{\"a}l{\"a} Foundation and affiliated with the University of Helsinki. She wishes to especially thank Steven Flores and Kalle Kyt{\"o}l{\"a} for many inspiring discussions and ideas. She has also enjoyed stimulating and helpful discussions with Michel Bauer, Dmitry Chelkak, Julien Dub{\'e}dat, Bertrand Duplantier, Philippe Di Francesco, Cl{\'e}ment Hongler, Konstantin Izyurov, Jesper Jacobsen, Fredrik Johansson-Viklund, Rinat Kedem, Antti Kemppainen, Jonatan Lenells, Jason Miller, Wei Qian, Hubert Saleur, and Hao Wu. She thanks Roland Friedrich for pointing out important references. Publisher Copyright: {\textcopyright} European Mathematical Society.",

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doi = "10.4171/AIHPD/81",

language = "English",

volume = "7",

pages = "1--73",

journal = "Annales de l'Institut Henri Poincare D: Combinatorics, Physics and their Interactions",

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AU - Peltola, Eveliina

N1 - Funding Information: Acknowledgments. During this work, the author was supported by Vilho, Yrjö and Kalle Väisälä Foundation and affiliated with the University of Helsinki. She wishes to especially thank Steven Flores and Kalle Kytölä for many inspiring discussions and ideas. She has also enjoyed stimulating and helpful discussions with Michel Bauer, Dmitry Chelkak, Julien Dubédat, Bertrand Duplantier, Philippe Di Francesco, Clément Hongler, Konstantin Izyurov, Jesper Jacobsen, Fredrik Johansson-Viklund, Rinat Kedem, Antti Kemppainen, Jonatan Lenells, Jason Miller, Wei Qian, Hubert Saleur, and Hao Wu. She thanks Roland Friedrich for pointing out important references. Publisher Copyright: © European Mathematical Society.

PY - 2020

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N2 - Applying the quantum group method developed in [50], we construct solutions to the Benoit & Saint-Aubin partial differential equations with boundary conditions given by specific recursive asymptotics properties. Our results generalize solutions constructed in [49, 55], known as the pure partition functions of multiple Schramm-Loewner evolutions. The generalization is reminiscent of fusion in conformal field theory, and our solutions can be thought of as partition functions of systems of random curves, where many curves may emerge from the same point.

AB - Applying the quantum group method developed in [50], we construct solutions to the Benoit & Saint-Aubin partial differential equations with boundary conditions given by specific recursive asymptotics properties. Our results generalize solutions constructed in [49, 55], known as the pure partition functions of multiple Schramm-Loewner evolutions. The generalization is reminiscent of fusion in conformal field theory, and our solutions can be thought of as partition functions of systems of random curves, where many curves may emerge from the same point.

KW - BPZ partial differential equations

KW - Conformal field theory (CFT)

KW - Loewner evolution (SLE)

KW - Quantum group

KW - Schramm

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DO - 10.4171/AIHPD/81

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IS - 1

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Basis for solutions of the Benoit & Saint-Aubin PDEs with particular asymptotics properties

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