Tachyon-massless couplings at order α′ in bosonic string theory

A bstract Recently, it has been proposed that the classical effective action of bosonic string theory should contain only couplings with an even number of tachyon fields. We employ the T-duality procedure to derive such couplings at order α ′ (four-derivative order) for the tachyon and massless fields. We first observe that, through higher-derivative field redefinitions of the tachyon potential term, one can choose a scheme in which — apart from the tachyon potential itself — all remaining couplings involve only covariant derivatives of the tachyon and the massless fields. We then construct a minimal basis of such couplings at four-derivative order, consisting of 14 independent terms. Imposing T-duality reduces this set to 6 nonzero couplings, expressed in terms of two unfixed parameters. One of these parameters is determined by matching to the known effective action in the zero-tachyon limit, while the other is fixed by comparison with the sphere-level S-matrix element of four tachyon vertex operators. This latter comparison also establishes that the coefficient of the T 4 term in the tachyon potential is positive. Remarkably, the tachyon mass term and this quartic term are consistent with a potential of the form (2/ α ′ )(– 1 + cos T ), which implies that the closed string tachyon condenses to the minimum of the potential at T = π , thereby generating an Anti-de Sitter spacetime with cosmological constant Λ = − 4/ α ′ .