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On integrable boundaries in the 2 dimensional O(N) σ-models

On integrable boundaries in the 2 dimensional O(N) σ-models
On integrable boundaries in the 2 dimensional O(N) σ-models
We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.
hep-th
0305-4470
Aniceto, Ines
0061ca0c-1ad8-4510-9b12-008e5c27a7ea
Bajnok, Zoltan
dfb5caba-a6c2-45fa-88d3-8ffc74961853
Gombor, Tamas
5792702d-056c-49bc-8093-d89e6724d689
Kim, Minkyoo
c694385d-6b48-4d3f-8b05-42813457586f
Palla, Laszlo
cdf70151-bf90-4154-963b-17110ec8e129
Aniceto, Ines
0061ca0c-1ad8-4510-9b12-008e5c27a7ea
Bajnok, Zoltan
dfb5caba-a6c2-45fa-88d3-8ffc74961853
Gombor, Tamas
5792702d-056c-49bc-8093-d89e6724d689
Kim, Minkyoo
c694385d-6b48-4d3f-8b05-42813457586f
Palla, Laszlo
cdf70151-bf90-4154-963b-17110ec8e129

Aniceto, Ines, Bajnok, Zoltan, Gombor, Tamas, Kim, Minkyoo and Palla, Laszlo (2017) On integrable boundaries in the 2 dimensional O(N) σ-models. Journal of Physics A: Mathematical and General, 50. (doi:10.1088/1751-8121/aa8205).

Record type: Article

Abstract

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.

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More information

Accepted/In Press date: 25 July 2017
Published date: 11 August 2017
Additional Information: Dedicated to the memory of Petr Kulish,
Keywords: hep-th

Identifiers

Local EPrints ID: 424139
URI: https://eprints.soton.ac.uk/id/eprint/424139
ISSN: 0305-4470
PURE UUID: a72a5aef-1fe6-4b29-b67b-08a2746be1e5

Catalogue record

Date deposited: 05 Oct 2018 11:30
Last modified: 27 Feb 2019 17:30

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