O(25, 25) symmetry of bosonic string theory at order $$\alpha '^2$$

It has been recently observed that the imposition of the O(1, 1) symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order $$\alpha '^2$$ α ′ 2 , up to an overall factor. In this paper, we use the cosmological reduction on the action and show that, up to one-dimensional field redefinitions and total derivative terms, it can be written in the O(25, 25)-invariant form proposed by Hohm and Zwiebach.