Xie, Xiao-Ning; Yue, Rui-Hong Lax connection of strings in \(\gamma\)-deformed backgrounds. (English) Zbl 1392.83089 Commun. Theor. Phys. 49, No. 5, 1265-1268 (2008). Summary: In this paper we consider classical strings propagating in \(\gamma\)-deformed AdS\(_3\times\) S\(^3\) backgrounds generated by TsT transformation on the AdS\(_3\) sector, which is described as the group manifold SL\((2,R)\), then we prove that the U\((1)\) currents of strings with the twisted boundary conditions are equal to those in \(\gamma\)-deformed backgrounds. Using TsT transformation, we can derive the local Lax connection and the monodromy matrix in \(\gamma\)-deformed backgrounds with the spectral parameter, which ensures the classical integrability of the string theories. MSC: 83E30 String and superstring theories in gravitational theory Keywords:TsT transformation; Lax connection; monodromy matrix; integrability PDFBibTeX XMLCite \textit{X.-N. Xie} and \textit{R.-H. Yue}, Commun. Theor. Phys. 49, No. 5, 1265--1268 (2008; Zbl 1392.83089) Full Text: DOI