Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics
Using recently proposed method of discrete Hirota dynamics for integrable (1+1)D quantum field theories on a finite space circle of length L we derive and test numerically a finite system of nonlinear integral equations for the exact spectrum of energies of SU(N)×SU(N) principal chiral field model a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2016-01-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321315003879 |
| _version_ | 1831654352450748416 |
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| author | Vladimir Kazakov Sébastien Leurent |
| author_facet | Vladimir Kazakov Sébastien Leurent |
| author_sort | Vladimir Kazakov |
| collection | DOAJ |
| description | Using recently proposed method of discrete Hirota dynamics for integrable (1+1)D quantum field theories on a finite space circle of length L we derive and test numerically a finite system of nonlinear integral equations for the exact spectrum of energies of SU(N)×SU(N) principal chiral field model as functions of mL, where m is the mass scale. We propose a determinant solution of the underlying Y-system, or Hirota equation, in terms of Wronskian determinants of N×N matrices parameterized by N−1 functions of the spectral parameter θ with the known analytic properties at finite L. Although the method works in principle for any state, the explicit equations are written for states in the U(1) sector only. For N>2, we encounter and clarify a few subtleties in these equations related to the presence of bound states, absent in the previously considered N=2 case. As a demonstration of efficiency of our method, we solve these equations numerically for a few low-lying states at N=3 in a wide range of mL. |
| first_indexed | 2024-12-19T16:26:14Z |
| format | Article |
| id | doaj.art-ed79d96746b94343b9384db4b72f135f |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-12-19T16:26:14Z |
| publishDate | 2016-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-ed79d96746b94343b9384db4b72f135f2022-12-21T20:14:20ZengElsevierNuclear Physics B0550-32131873-15622016-01-01902C35438610.1016/j.nuclphysb.2015.11.012Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamicsVladimir Kazakov0Sébastien Leurent1Ecole Normale Superieure, LPT, 75231 Paris Cedex-5, FranceEcole Normale Superieure, LPT, 75231 Paris Cedex-5, FranceUsing recently proposed method of discrete Hirota dynamics for integrable (1+1)D quantum field theories on a finite space circle of length L we derive and test numerically a finite system of nonlinear integral equations for the exact spectrum of energies of SU(N)×SU(N) principal chiral field model as functions of mL, where m is the mass scale. We propose a determinant solution of the underlying Y-system, or Hirota equation, in terms of Wronskian determinants of N×N matrices parameterized by N−1 functions of the spectral parameter θ with the known analytic properties at finite L. Although the method works in principle for any state, the explicit equations are written for states in the U(1) sector only. For N>2, we encounter and clarify a few subtleties in these equations related to the presence of bound states, absent in the previously considered N=2 case. As a demonstration of efficiency of our method, we solve these equations numerically for a few low-lying states at N=3 in a wide range of mL.http://www.sciencedirect.com/science/article/pii/S0550321315003879 |
| spellingShingle | Vladimir Kazakov Sébastien Leurent Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics Nuclear Physics B |
| title | Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics |
| title_full | Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics |
| title_fullStr | Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics |
| title_full_unstemmed | Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics |
| title_short | Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics |
| title_sort | finite size spectrum of su n principal chiral field from discrete hirota dynamics |
| url | http://www.sciencedirect.com/science/article/pii/S0550321315003879 |
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