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The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.``