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

Recently, it has been shown that the gauge invariance requires the minimum number of independent couplings for $B$-field, metric and dilaton at order $α'^2$ to be 60. In this paper we fix the corresponding 60 parameters in string theory by requiring the couplings to be invariant under the global T-duality transformations. The Riemann cubed terms are exactly the same as the couplings that have been found by the S-matrix calculations.

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