Normalization of D-instanton Amplitudes

Abstract

D-instanton amplitudes suffer from various infrared divergences associated with tachyonic or massless open string modes, leading to ambiguous contribution to string amplitudes. It has been shown previously that string field theory can resolve these ambiguities and lead to unambiguous expressions for D-instanton contributions to string amplitudes, except for an overall normalization constant that remains undetermined. In this paper we show that string field theory, together with the world-sheet description of the amplitudes, can also fix this normalization constant. We apply our analysis to the special case of two dimensional string theory, obtaining results in agreement with the matrix model results obtained by Balthazar, Rodriguez and Yin.

Normalization of Type IIB D-instanton Amplitudes

“…The general procedure for computing the normalization of the D-instanton amplitude was described in [31]. As in [31], we shall formally write the normalization N as:…”

“…Nevertheless the cancellation in the L 0 > 0 sector shows that the contribution to N comes entirely from the zero mode sector. Our strategy, following [31], will be to represent the zero mode contribution to N as integrals over the zero mode string fields, and then explicitly carry out these integrals.…”

“…Our next task is to find the relation between ξ µ and the D-instanton locations ξ µ along the Euclidean space-time. This analysis proceeds as in [31]. We note that the integrated, zero picture vertex operators associated with the mode ξ µ is given by…”

“…Many D-instanton induced terms were predicted using S-duality invariances of various compactified string theories , but except for the early attempts [2], the direct systematic computation of these amplitudes from first principles has not been carried out. However during the last two years progress was made in the context of two dimensional string theory [26][27][28][29][30][31]. In particular, [26,27] computed the precise contributions to the amplitudes from D-instantons in terms of some constants that appear to be divergent in the world-sheet formalism.…”

“…In particular, [26,27] computed the precise contributions to the amplitudes from D-instantons in terms of some constants that appear to be divergent in the world-sheet formalism. It was then found that string field theory gives finite, unambiguous values of these constants [28][29][30][31].…”