D-instanton induced superpotential

Abstract

We use string field theory to fix the normalization of the D-instanton corrections to the superpotential involving the moduli fields of type II string theory compactified on an orientifold of a Calabi-Yau threefold in the absence of fluxes. We focus on O(1) instantons whose only zero modes are the four bosonic modes associated with translation of the instanton in non-compact directions and a pair of fermionic zero modes associated with the two supercharges broken by the instanton. We work with a generic superconformal field theory and express our answer in terms of the spectrum of open strings on the instanton. We analyse the contribution of multi-instantons of this kind to the superpotential and argue that it vanishes when background fluxes are absent.

Normalization of ZZ instanton amplitudes in minimal string theory

“…It is testament to this philosophy that the original ideas in Refs. [6,7,8], which were developed in the context of two-dimensional string theory, have been generalized to tackle various nonperturbative effects in critical 10-d superstring theory and its compactifications [15,16,17,18,19,20], leading to highly nontrivial checks of superstring dualities. For instance, Ref.…”

A worldsheet description of flux compactifications

“…While our discussion in this work primarily focused on string perturbation theory, it is important to note that SFT has demonstrated remarkable power in the recent exploration of non-perturbative D-instanton effects [63,64,[101][102][103][104][105][106][107][108][109][110][111][112]. The suitability of SFT for Dinstantons arises from its ability to systematically integrate out open string fields on the D-instanton, resulting in the effective field theory for the dynamic closed string fields.…”

“…As an illustration of the potential of SFT in this context, in [108] the overall numerical factor of the non-perturbative superpotential was fixed by regulating the IR divergence arising from the zero modes of Euclidean D-branes appearing in fluxless orientifold compactifications. Shortly after, the massive state contribution to the one-loop pfaffian was shown to be determined by open-unoriented topological string partition function at one-loop [113].…”

Normalization of D instanton amplitudes in two dimensional type 0B string theory

“…In recent years string field theory has proved to be a useful tool in dealing with infrared divergences in the open string theory on the D-instanton, including in the annulus zero point function -see e.g. [4][5][6][7][8][9][10][11]. These papers computed similar normalization factors that are left undetermined in the world-sheet description [12][13][14].…”