Fiki T. Akbar, Bobby E. Gunara, Triyanta, Freddy P. Zen
In this paper, we prove the local existence of the bosonic part of N=1 supersymmetric gauge theory in four dimensions with general couplings. We start with the Lagrangian of generally coupled vector and chiral multiplets with scalar potential turned on. Then, for the sake of simplicity, we set all fermions vanish at the level of equations of motions, so we only have the bosonic parts of the theory. We apply Segal's general theory to show the local existence of solutions of field equations of motions by taking K\"ahler potential to be bounded above by U(n) symmetric K\"ahler potential and the first derivative of gauge couplings to be at most linear growth functions.
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http://arxiv.org/abs/1302.4212
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