On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$-models

Aniceto, Ines; Bajnok, Zoltan; Gombor, Tamas; Kim, Minkyoo; Palla, Laszlo

doi:10.1088/1751-8121/aa8205

On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$ -models

Jun 16, 2017

34 pages

Published in:

J.Phys.A 50 (2017) 36, 364002

Published: Aug 11, 2017

e-Print:

1706.05221 [hep-th]

DOI:

10.1088/1751-8121/aa8205

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Abstract: (IOP)

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear

O(N)

σ-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.

Note:

Dedicated to the memory of Petr Kulish, 31 pages, 1 figure, v2: conformality and integrability of the boundary conditions are distinguished

integrable boundary conditions
O(N) models
boundary Lax formulation
boundary Bethe–Yang equations
integrability
spectral
O(N)
Yang-Baxter equation
boundary condition
conservation law

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

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On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$ -models