nLab Brownian loop soup

Idea

(…)

Related entries

• Brownian motion

• conformal field theory

• loop space

References

The original article:

• Gregory F. Lawler, Wendelin Werner, The Brownian loop soup, Probab. Th. Rel. Fields 128 (2004) 565-588 [arXiv:math/0304419, doi:10.1007/s00440-003-0319-6]

Relation to conformal field theory:

• Federico Camia, Valentino Foit, Alberto Gandolfi, Matthew Kleban, Scalar conformal primary fields in the Brownian loop soup [arXiv:2109.12116]

• Federico Camia, Valentino Foit, Alberto Gandolfi, Matthew Kleban, The Brownian loop soup stress-energy tensor [arXiv:2112.00074, doi:10.1007/JHEP11(2022)009]

Review:

• Valentino Foit: Brownian loops and conformally invariant systems, talk at CQTS (Nov 2022) [pdf, video: rec]

Further discussion:

• Amin Moharramipour, Dan Sehayek, Thomas Scaffidi, Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories [arXiv:2310.00037]

• Rongvoram Nivesvivat, Sylvain Ribault, Jesper L. Jacobsen, Critical loop models are exactly solvable, SciPost Phys. 17 029 (2024) [arXiv:2311.17558, doi:10.21468/SciPostPhys.17.2.029]

• Linnea Grans-Samuelsson, Jesper L. Jacobsen, Rongvoram Nivesvivat, Sylvain Ribault, Hubert Saleur: From combinatorial maps to correlation functions in loop models, SciPost Phys. 15 147 (2023) [arXiv:2302.08168, doi:10.21468/SciPostPhys.15.4.147]

• Federico Camia, Rongvoram Nivesvivat: Boundary operators in the Brownian loop soup [arXiv:2601.02755]

Review:

• Rongvoram Nivesvivat: Three-point connectivities of interfaces in 2D critical statistical models talk at CQTS (30 Apr 2025) [slides: pdf]

In relation to superspheres:

• Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur, Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups, J. Phys. A: Math. Theor. 52 345001 (2019) [doi:10.1088/1751-8121/ab2aaa, arXiv:1810.07807]