Classical integrability of strings in $\gamma$-deformed backgrounds
Xie Xiao-Ning (解小宁)ac, Yue Rui-Hong (岳瑞宏)bc
aSKLLQG, 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
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.
Received: 09 August 2007
Revised: 02 March 2008
Accepted manuscript online:
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