The random free field scalar theory

Abstract Quantum field theories with quenched disorder are so hard to study that even exactly solvable free theories present puzzling aspects. We consider a free scalar field ϕ in d dimensions coupled to a random source h with quenched disorder. Despite the presence of a mass scale governing the dis...

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Main Authors: Alessandro Piazza, Marco Serone, Emilio Trevisani
Format: Article
Language:English
Published: SpringerOpen 2025-08-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP08(2025)072
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author Alessandro Piazza
Marco Serone
Emilio Trevisani
author_facet Alessandro Piazza
Marco Serone
Emilio Trevisani
author_sort Alessandro Piazza
collection DOAJ
description Abstract Quantum field theories with quenched disorder are so hard to study that even exactly solvable free theories present puzzling aspects. We consider a free scalar field ϕ in d dimensions coupled to a random source h with quenched disorder. Despite the presence of a mass scale governing the disorder distribution, we derive a new description of the theory that allows us to show that the theory is gapless and invariant under conformal symmetry, which acts in a non-trivial way on ϕ and h. This manifest CFT description reveals the presence of exotic continuous symmetries, such as nilpotent bosonic ones, in the quenched theory. We also reconsider Cardy’s CFT description defined through the replica trick. In this description, the nilpotent symmetries reveal a striking resemblance with Parisi-Sourlas supersymmetries. We provide explicit maps of correlation functions between such CFTs and the original quenched theory. The maps are non-trivial and show that conformal behaviour is manifest only when considering suitable linear combinations of averages of products of correlators. We also briefly discuss how familiar notions like normal ordering of composite operators and OPE can be generalized in the presence of the more complicated local observables in the quenched theory.
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spelling doaj-art-da28293eca314dcdbe211feb71c100372025-08-20T03:42:43ZengSpringerOpenJournal of High Energy Physics1029-84792025-08-012025815110.1007/JHEP08(2025)072The random free field scalar theoryAlessandro Piazza0Marco Serone1Emilio Trevisani2SISSASISSALaboratoire de Physique Théorique et Hautes Énergies, CNRS & Sorbonne UniversitéAbstract Quantum field theories with quenched disorder are so hard to study that even exactly solvable free theories present puzzling aspects. We consider a free scalar field ϕ in d dimensions coupled to a random source h with quenched disorder. Despite the presence of a mass scale governing the disorder distribution, we derive a new description of the theory that allows us to show that the theory is gapless and invariant under conformal symmetry, which acts in a non-trivial way on ϕ and h. This manifest CFT description reveals the presence of exotic continuous symmetries, such as nilpotent bosonic ones, in the quenched theory. We also reconsider Cardy’s CFT description defined through the replica trick. In this description, the nilpotent symmetries reveal a striking resemblance with Parisi-Sourlas supersymmetries. We provide explicit maps of correlation functions between such CFTs and the original quenched theory. The maps are non-trivial and show that conformal behaviour is manifest only when considering suitable linear combinations of averages of products of correlators. We also briefly discuss how familiar notions like normal ordering of composite operators and OPE can be generalized in the presence of the more complicated local observables in the quenched theory.https://doi.org/10.1007/JHEP08(2025)072Conformal and W SymmetryScale and Conformal Symmetries
spellingShingle Alessandro Piazza
Marco Serone
Emilio Trevisani
The random free field scalar theory
Journal of High Energy Physics
Conformal and W Symmetry
Scale and Conformal Symmetries
title The random free field scalar theory
title_full The random free field scalar theory
title_fullStr The random free field scalar theory
title_full_unstemmed The random free field scalar theory
title_short The random free field scalar theory
title_sort random free field scalar theory
topic Conformal and W Symmetry
Scale and Conformal Symmetries
url https://doi.org/10.1007/JHEP08(2025)072
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