No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

The full text of this article is not currently available.

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

/content/aip/journal/jmp/55/6/10.1063/1.4880341

http://aip.metastore.ingenta.com/content/aip/journal/jmp/55/6/10.1063/1.4880341

Article metrics loading...

/content/aip/journal/jmp/55/6/10.1063/1.4880341

2014-06-05

2016-09-25

Full text loading...

###
Most read this month

Article

content/aip/journal/jmp

Journal

5

3

Commenting has been disabled for this content