Nonrelativistic Dirac fermions on the torus

Autores
Aguilera Damia, Jeremías; Solís Delgadillo, Juan Mario; Torroba, Gonzalo
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Two dimensional conformal feld theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories.
Fil: Aguilera Damia, Jeremías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Université Libre de Bruxelles; Bélgica
Fil: Solís Delgadillo, Juan Mario. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Materia
NONRELATIVISTIC
FERMIONS
FINITE DENSITY
MODULAR
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/231858
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Nonrelativistic Dirac fermions on the torusAguilera Damia, JeremíasSolís Delgadillo, Juan MarioTorroba, GonzaloNONRELATIVISTICFERMIONSFINITE DENSITYMODULARhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Two dimensional conformal feld theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories.Fil: Aguilera Damia, Jeremías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Université Libre de Bruxelles; BélgicaFil: Solís Delgadillo, Juan Mario. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaSpringer2023-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/231858Aguilera Damia, Jeremías; Solís Delgadillo, Juan Mario; Torroba, Gonzalo; Nonrelativistic Dirac fermions on the torus; Springer; Journal of High Energy Physics; 2023; 12; 12-2023; 1-211029-8479CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/JHEP12(2023)060info:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP12(2023)060info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:04:42Zoai:ri.conicet.gov.ar:11336/231858instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:04:42.535CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nonrelativistic Dirac fermions on the torus
title Nonrelativistic Dirac fermions on the torus
spellingShingle Nonrelativistic Dirac fermions on the torus
Aguilera Damia, Jeremías
NONRELATIVISTIC
FERMIONS
FINITE DENSITY
MODULAR
title_short Nonrelativistic Dirac fermions on the torus
title_full Nonrelativistic Dirac fermions on the torus
title_fullStr Nonrelativistic Dirac fermions on the torus
title_full_unstemmed Nonrelativistic Dirac fermions on the torus
title_sort Nonrelativistic Dirac fermions on the torus
dc.creator.none.fl_str_mv Aguilera Damia, Jeremías
Solís Delgadillo, Juan Mario
Torroba, Gonzalo
author Aguilera Damia, Jeremías
author_facet Aguilera Damia, Jeremías
Solís Delgadillo, Juan Mario
Torroba, Gonzalo
author_role author
author2 Solís Delgadillo, Juan Mario
Torroba, Gonzalo
author2_role author
author
dc.subject.none.fl_str_mv NONRELATIVISTIC
FERMIONS
FINITE DENSITY
MODULAR
topic NONRELATIVISTIC
FERMIONS
FINITE DENSITY
MODULAR
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Two dimensional conformal feld theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories.
Fil: Aguilera Damia, Jeremías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Université Libre de Bruxelles; Bélgica
Fil: Solís Delgadillo, Juan Mario. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
description Two dimensional conformal feld theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories.
publishDate 2023
dc.date.none.fl_str_mv 2023-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/231858
Aguilera Damia, Jeremías; Solís Delgadillo, Juan Mario; Torroba, Gonzalo; Nonrelativistic Dirac fermions on the torus; Springer; Journal of High Energy Physics; 2023; 12; 12-2023; 1-21
1029-8479
CONICET Digital
CONICET
url http://hdl.handle.net/11336/231858
identifier_str_mv Aguilera Damia, Jeremías; Solís Delgadillo, Juan Mario; Torroba, Gonzalo; Nonrelativistic Dirac fermions on the torus; Springer; Journal of High Energy Physics; 2023; 12; 12-2023; 1-21
1029-8479
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/JHEP12(2023)060
info:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP12(2023)060
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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