receives quantum corrections, and the instantons correspond to Euclidean $p$-branes wrapping $p+1$ cycles of the CY [@BBS].

The simplest setup for studying this problem, is to consider CY-compactifications of M-theory/type IIA superstrings with Hodge number $h_{2,1}=0$, or, for type IIB, $h_{1,1}=0$ [^1], since this yields a low-energy effective action of $N=2$ supergravity coupled to a single hypermultiplet, such that the moduli space ${\cal M}_H$ has dimension four. From a type IIB perspective, this hypermultiplet arises from dualizing the *double-tensor* multiplet, whose bosonic components descend from the $NS$-$NS$ and $R$-$R$ two-forms and scalars in ten dimensions. This suggests that instanton calculations should be done on the double-tensor multiplet side. In the next section, we shall make another argument, which also applies to type IIA and M-theory, why the double-tensor multiplet is more appropriate for our purposes.

Yet, even in the case of a single hypermultiplet, it is difficult to compute instanton effects directly in string theory, without explicit knowledge of the instanton measure and the details of the wrapped branes along the CY cycles. Therefore, we will study this problem in a pure supergravity context, in which semi-classical instanton calculations can be done in the more conventional and “field-theoretic” way, following 