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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/231858
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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 Técnicas2025-09-29T09:36:35Zoai: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:34982025-09-29 09:36:35.415CONICET 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 |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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