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It was proved more than three decades ago, that the first order $\alpha'$correction of string effective theory could be written as the Gauss-Bonnetterm, which is the quadratic term of Lovelock gravity. In cosmologicalbackground, with an appropriate field redefinition, we reorganize the infinite$\alpha'$ corrections of string effective action into a finite term expressionfor any specific dimension. This finite term expression matches Lovelockgravity exactly and thus fix the couplings of Lovelock gravity by thecoefficients of string effective action. This result thus provides a strongsupport to string theory.

Derive Lovelock Gravity from String Theory in Cosmological Background