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Recently, it has been shown that the gauge invariance requires the minimumnumber of independent couplings for $B$-field, metric and dilaton at order$\alpha'^2$ to be 60. In this paper we fix the corresponding 60 parameters instring theory by requiring the couplings to be invariant under the globalT-duality transformations. The Riemann cubed terms are exactly the same as thecouplings that have been found by the S-matrix calculations.

Effective action of bosonic string theory at order $ \alpha'^2 $