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Lax connection of strings in \(\gamma\)-deformed backgrounds. (English) Zbl 1392.83089

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
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