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A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models

### Abstract

We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S^{3} and the isometry is SU (2)L × U(1)R. It is known that SU (2)L is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1)R is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices. The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.

© 2014 AIP Publishing LLC

Received 20 February 2014
Accepted 16 May 2014
Published online 05 June 2014

Acknowledgments:
We would like to thank Takuya Matsumoto for useful discussions. The work of I.K. was supported by the Japan Society for the Promotion of Science (JSPS).

Article outline:

I. INTRODUCTION
II. PRELIMINARY
A. Squashed S^{3}
B. The classical action of the squashed WZNW models
III. THE LEFT DESCRIPTION
A. Lax pairs
B. Yangians
IV. THE RIGHT DESCRIPTION
A. Lax pair
1. Monodromy matrix
B. *q*-deformation of * su *(2)_{R}
C. Expansions of the monodromy matrix
1. Expansion around Reλ_{ R } = −∞
2. Expansion around Reλ_{ R } = +∞
D. An infinite-dimensional extension of *q*-deformed * su *(2)_{R}
E. The *r*/*s*-matrices
V. THE LEFT-RIGHT DUALITY
A. The fundamental domains of the spectral parameters
B. The reduced right descriptions
1. A relation of the spectral parameters
C. The gauge equivalence
1. Summary
2. The gauge transformation of the *r*/*s*-matrices
VI. THE DEGENERATE LIMITS
A. α = 0
B. α = π*i*/2
VII. CONCLUSION AND DISCUSSION

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2014-06-05

2016-10-22

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