nLab worldsheet instanton

Idea

In perturbative string theory, worldsheet instantons are contributions to the string scattering amplitudes of sigma-model (i.e. “geometric”) perturbative string theory vacua which correspond to worldsheet configurations that may not be connected continuously to configurations constant on a point, hence which wrap some 2-cycle in the target spacetime.

Worldsheet instantons contribute non-perturbative effects to the string scattering amplitudes with respect to the string length scale $\ell_s$, see there.

In contrast, non-perturbative contributions to string scattering amplitudes $g_s$ in the string coupling constant come from D-brane instantons.

These two kinds of stringy non-perturbative effects unify under the duality between M-theory and type IIA string theory to membrane instantons, depending on whether the M2-brane configuration wraps the M-theory circle fiber $S^1_{10}$ or not, see there.

Yukawa couplings in intersecting D-brane models

In intersecting D-brane models Yukawa couplings are encoded by worldsheet instantons of open strings stretching between the intersecting D-branes (see Marchesano 03, Section 7.5). Mathematically this is encoded by derived hom-spaces in a Fukaya category (see Marchesano 03, Section 7.5).

table grabbed from Marchesano 03

References

In intersecting D-brane models:

• Fernando Marchesano, section 7.1.1 of Intersecting D-brane Models (arXiv:hep-th/0307252)