中国物理B ›› 2008, Vol. 17 ›› Issue (11): 4153-4157.doi: 10.1088/1674-1056/17/11/032

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Classical integrability of strings in γ-deformed backgrounds

岳瑞宏1, 解小宁2   

  1. (1)Department of Physics, Ningbo University, Ningbo 315211, China;Institute of Modern Physics, Northwest University, Xi'an 710069, China; (2)SKLLQG, Institute of Earth Environment, Chinese Academy of Sciences, Xi'an 710075, China;Institute of Modern Physics, Northwest University, Xi'an 710069, China
  • 收稿日期:2007-08-09 修回日期:2008-03-02 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 90403019 and 10575080).

Classical integrability of strings in $\gamma$-deformed backgrounds

Xie Xiao-Ning (解小宁)ac, Yue Rui-Hong (岳瑞宏)bc    

  1. a SKLLQG, Institute of Earth Environment, Chinese Academy of Sciences, Xi'an 710075, China; b Department of Physics, Ningbo University, Ningbo 315211, China; b Institute of Modern Physics, Northwest University, Xi'an 710069, China
  • Received:2007-08-09 Revised:2008-03-02 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 90403019 and 10575080).

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摘要： This paper considers classical strings propagating in $\gamma$-deformed $AdS_3\times S^3$ backgrounds generated by certain shift T-dualities accompanied (TsT) transformations on $S^3$ and $AdS_3$, respectively. It finds that the $U(1)$ currents of strings with the twisted boundary conditions are equal to those in $\gamma$-deformed backgrounds generated by TsT transformations on both $S^3$ and $AdS_3$. Applying the TsT transformations, it derives the local Lax connections and the monodromy matrices in $\gamma$-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.

关键词: TsT transformation, Lax connection, monodromy matrix, integrability

Abstract: This paper considers classical strings propagating in $\gamma$-deformed $AdS_3\times S^3$ backgrounds generated by certain shift T-dualities accompanied (TsT) transformations on $S^3$ and $AdS_3$, respectively. It finds that the $U(1)$ currents of strings with the twisted boundary conditions are equal to those in $\gamma$-deformed backgrounds generated by TsT transformations on both $S^3$ and $AdS_3$. Applying the TsT transformations, it derives the local Lax connections and the monodromy matrices in $\gamma$-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.

Key words: TsT transformation, Lax connection, monodromy matrix, integrability

中图分类号:  (Strings and branes)

  • 11.25.-w
11.10.Lm (Nonlinear or nonlocal theories and models) 11.15.-q (Gauge field theories)