Lattice regularisation of a non-compact boundary conformal field theory
Abstract Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such CFTs have been identified as the continuum limits of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2021)180 |
| _version_ | 1818409500556656640 |
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| author | Niall F. Robertson Jesper Lykke Jacobsen Hubert Saleur |
| author_facet | Niall F. Robertson Jesper Lykke Jacobsen Hubert Saleur |
| author_sort | Niall F. Robertson |
| collection | DOAJ |
| description | Abstract Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such CFTs have been identified as the continuum limits of lattice models with a finite number of degrees of freedom per site. However, results have so far been restricted to the case of periodic boundary conditions, precluding the exploration via lattice models of aspects of non-compact boundary CFTs and the corresponding D-brane constructions. The present paper follows a series of previous works on a ℤ2-staggered XXZ spin chain, whose continuum limit is known to be a non-compact CFT related with the Euclidian black hole sigma model. By using the relationship of this spin chain with an integrable D 2 2 $$ {D}_2^2 $$ vertex model, we here identify integrable boundary conditions that lead to a continuous spectrum of boundary exponents, and thus correspond to non-compact branes. In the context of the Potts model on a square lattice, they correspond to wired boundary conditions at the physical antiferromagnetic critical point. The relations with the boundary parafermion theories are discussed as well. We are also able to identify a boundary renormalisation group flow from the non-compact boundary conditions to the previously studied compact ones. |
| first_indexed | 2024-12-14T10:00:37Z |
| format | Article |
| id | doaj.art-bdf61bc998834986a42c0c2a5033a729 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T10:00:37Z |
| publishDate | 2021-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-bdf61bc998834986a42c0c2a5033a7292022-12-21T23:07:17ZengSpringerOpenJournal of High Energy Physics1029-84792021-02-012021214010.1007/JHEP02(2021)180Lattice regularisation of a non-compact boundary conformal field theoryNiall F. Robertson0Jesper Lykke Jacobsen1Hubert Saleur2Université Paris Saclay, CNRS, CEA, Institut de Physique ThéoriqueUniversité Paris Saclay, CNRS, CEA, Institut de Physique ThéoriqueUniversité Paris Saclay, CNRS, CEA, Institut de Physique ThéoriqueAbstract Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such CFTs have been identified as the continuum limits of lattice models with a finite number of degrees of freedom per site. However, results have so far been restricted to the case of periodic boundary conditions, precluding the exploration via lattice models of aspects of non-compact boundary CFTs and the corresponding D-brane constructions. The present paper follows a series of previous works on a ℤ2-staggered XXZ spin chain, whose continuum limit is known to be a non-compact CFT related with the Euclidian black hole sigma model. By using the relationship of this spin chain with an integrable D 2 2 $$ {D}_2^2 $$ vertex model, we here identify integrable boundary conditions that lead to a continuous spectrum of boundary exponents, and thus correspond to non-compact branes. In the context of the Potts model on a square lattice, they correspond to wired boundary conditions at the physical antiferromagnetic critical point. The relations with the boundary parafermion theories are discussed as well. We are also able to identify a boundary renormalisation group flow from the non-compact boundary conditions to the previously studied compact ones.https://doi.org/10.1007/JHEP02(2021)180Bethe AnsatzBoundary Quantum Field TheoryConformal Field TheoryBlack Holes in String Theory |
| spellingShingle | Niall F. Robertson Jesper Lykke Jacobsen Hubert Saleur Lattice regularisation of a non-compact boundary conformal field theory Journal of High Energy Physics Bethe Ansatz Boundary Quantum Field Theory Conformal Field Theory Black Holes in String Theory |
| title | Lattice regularisation of a non-compact boundary conformal field theory |
| title_full | Lattice regularisation of a non-compact boundary conformal field theory |
| title_fullStr | Lattice regularisation of a non-compact boundary conformal field theory |
| title_full_unstemmed | Lattice regularisation of a non-compact boundary conformal field theory |
| title_short | Lattice regularisation of a non-compact boundary conformal field theory |
| title_sort | lattice regularisation of a non compact boundary conformal field theory |
| topic | Bethe Ansatz Boundary Quantum Field Theory Conformal Field Theory Black Holes in String Theory |
| url | https://doi.org/10.1007/JHEP02(2021)180 |
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