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The minimal Starobinsky supergravity with the inflaton (scalaron) and the goldstino in a massive vector supermultiplet is coupled to the dilaton-axion chiral superfield with the no-scale K\"ahler potential and a superpotential.
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S. Kachru, R. Kallosh, A. D. Linde and S. P. Trivedi, ”De Sitter vacua in string theory”, Phys. Rev. D68
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