FZZT Brane Relations in the Presence of Boundary Magnetic Fields
We show how a boundary state different from the (1,1) Cardy state may be realised in the (m,m+1) minimal string by the introduction of an auxiliary matrix into the standard two hermitian matrix model. This boundary is a natural generalisation of the free spin boundary state in the Ising model. The r...
| Váldodahkkit: | , |
|---|---|
| Materiálatiipa: | Journal article |
| Giella: | English |
| Almmustuhtton: |
2012
|
| _version_ | 1826302499963797504 |
|---|---|
| author | Atkin, MR Zohren, S |
| author_facet | Atkin, MR Zohren, S |
| author_sort | Atkin, MR |
| collection | OXFORD |
| description | We show how a boundary state different from the (1,1) Cardy state may be realised in the (m,m+1) minimal string by the introduction of an auxiliary matrix into the standard two hermitian matrix model. This boundary is a natural generalisation of the free spin boundary state in the Ising model. The resolvent for the auxiliary matrix is computed using an extension of the saddle-point method of Zinn-Justin to the case of non-identical potentials. The structure of the saddle-point equations result in a Seiberg-Shih like relation between the boundary states which is valid away from the continuum limit, in addition to an expression for the spectral curve of the free spin boundary state. We then show how the technique may be used to analyse boundary states corresponding to a boundary magnetic field, thereby allowing us to generalise the work of Carroll et al. on the boundary renormalisation flow of the Ising model, to any (m,m+1) model. |
| first_indexed | 2024-03-07T05:48:29Z |
| format | Journal article |
| id | oxford-uuid:e804f52b-5087-41da-a6e1-e6e504e842a6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:48:29Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:e804f52b-5087-41da-a6e1-e6e504e842a62022-03-27T10:43:31ZFZZT Brane Relations in the Presence of Boundary Magnetic FieldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e804f52b-5087-41da-a6e1-e6e504e842a6EnglishSymplectic Elements at Oxford2012Atkin, MRZohren, SWe show how a boundary state different from the (1,1) Cardy state may be realised in the (m,m+1) minimal string by the introduction of an auxiliary matrix into the standard two hermitian matrix model. This boundary is a natural generalisation of the free spin boundary state in the Ising model. The resolvent for the auxiliary matrix is computed using an extension of the saddle-point method of Zinn-Justin to the case of non-identical potentials. The structure of the saddle-point equations result in a Seiberg-Shih like relation between the boundary states which is valid away from the continuum limit, in addition to an expression for the spectral curve of the free spin boundary state. We then show how the technique may be used to analyse boundary states corresponding to a boundary magnetic field, thereby allowing us to generalise the work of Carroll et al. on the boundary renormalisation flow of the Ising model, to any (m,m+1) model. |
| spellingShingle | Atkin, MR Zohren, S FZZT Brane Relations in the Presence of Boundary Magnetic Fields |
| title | FZZT Brane Relations in the Presence of Boundary Magnetic Fields |
| title_full | FZZT Brane Relations in the Presence of Boundary Magnetic Fields |
| title_fullStr | FZZT Brane Relations in the Presence of Boundary Magnetic Fields |
| title_full_unstemmed | FZZT Brane Relations in the Presence of Boundary Magnetic Fields |
| title_short | FZZT Brane Relations in the Presence of Boundary Magnetic Fields |
| title_sort | fzzt brane relations in the presence of boundary magnetic fields |
| work_keys_str_mv | AT atkinmr fzztbranerelationsinthepresenceofboundarymagneticfields AT zohrens fzztbranerelationsinthepresenceofboundarymagneticfields |