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The spectral problem of spin chains in N=2 quiver gauge theories
Thesis (PhD (Physics))--University of Pretoria, 2021.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2021
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| _version_ | 1867613520472834048 |
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| access_status_str | Open Access |
| author2 | Zoubos, Konstantinos |
| author_browse | Zoubos, Konstantinos |
| author_facet | Zoubos, Konstantinos |
| collection | Thesis |
| dc_rights_str_mv | © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (PhD (Physics))--University of Pretoria, 2021. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/83069 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:27.405Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/83069 The spectral problem of spin chains in N=2 quiver gauge theories Zoubos, Konstantinos randlerabe@gmail.com Rabe, Randle Conformal field theory Spin chains Integrability Supersymmetry Coordinate Bethe ansatz UCTD Thesis (PhD (Physics))--University of Pretoria, 2021. We investigate the spectral problem of spin chain models in a family of 4D N =2 superconformal quiver gauge theories, constructed as an orbifold of N = 4 super Yang-Mills theory, in the planar limit. We consider two scalar subsectors, namely, the dense XY sector (constructed out of scalar fields in the bifundamental representation of the gauge groups) and the dilute XZ sector (constructed out of scalar fields in the bifundamental and adjoint representations of the gauge groups). At one-loop level, we show that the XY sector can be mapped to an alternating-bond spin chain model and that the XZ sector can be mapped to a dynamical Temperley-Lieb spin chain model. Using the coordinate Bethe ansatz and techniques from alternating-bond spin chains, we are able to solve the eigenvalue problem for both sectors up to the two magnon level by enhancing the usual Bethe wavefunctions with an extra set of momenta that is not a permutation of the original set of momenta. Thus, the two magnon sector already exhibits diffractive scattering. The solutions exhibit rich physics and properties, such as two scattering matrices and a ratio function, which we study in detail. The dispersion relation, which is shared by both scalar subsectors, can be naturally parametrised using elliptic functions. Finally, given our solution for the two magnon problem, we discuss the challenges that arise in attempting to extend the construction of the wavefunctions to the three magnon problem, as well as the notion of quantum integrability within our scalar subsectors. National Institute for Theoretical Physics (NITheP) University of Pretoria Physics PhD (Physics) Unrestricted 2021-12-15T13:46:10Z 2021-12-15T13:46:10Z 2022 2021 Thesis Rabe, R 2021, The spectral problem of spin chains in N=2 quiver gauge theories, PhD thesis, University of Pretoria, Pretoria, viewed 211214 http://hdl.handle.net/2263/31804 A2022 http://hdl.handle.net/2263/83069 en © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Conformal field theory Spin chains Integrability Supersymmetry Coordinate Bethe ansatz UCTD The spectral problem of spin chains in N=2 quiver gauge theories |
| title | The spectral problem of spin chains in N=2 quiver gauge theories |
| title_full | The spectral problem of spin chains in N=2 quiver gauge theories |
| title_fullStr | The spectral problem of spin chains in N=2 quiver gauge theories |
| title_full_unstemmed | The spectral problem of spin chains in N=2 quiver gauge theories |
| title_short | The spectral problem of spin chains in N=2 quiver gauge theories |
| title_sort | spectral problem of spin chains in n 2 quiver gauge theories |
| topic | Conformal field theory Spin chains Integrability Supersymmetry Coordinate Bethe ansatz UCTD |
| url | http://hdl.handle.net/2263/83069 |