Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings

Abstract

In the previous papers, it is pointed out that a supersymmetric double-well matrix model corresponds to a two-dimensional type IIA superstring theory on a Ramond-Ramond background at the level of correlation functions. This was confirmed by agreement between their planar correlation functions. The supersymmetry in the matrix model corresponds to the target space supersymmetry and it is shown to be spontaneously broken by nonperturbative effect. Furthermore, in the matrix model we computed one-point functions of single-trace operators to all order of genus expansion in its double scaling limit. We found that this expansion is stringy and not Borel summable and hence there arises an ambiguity in applying the Borel resummation technique. We confirmed that resurgence works here, namely this ambiguity in perturbative series in a zero-instanton sector is exactly canceled by another ambiguity in a one-instanton sector obtained by instanton calculation. In this paper we extend this analysis and study resurgence structure of the two-point functions of the single trace operators. By using results in the random matrix theory, we derive two-point functions at arbitrary genus and see that the perturbative series in the zero-instanton sector again has an ambiguity. We find that the two-point functions inevitably have logarithmic singularity even at higher genus. In this derivation we obtain a new result of the two-point function expressed by the one-point function at the leading order in the soft-edge scaling limit of the random matrix theory. We also compute an ambiguity in the one-instanton sector by using the Airy kernel, and confirm that ambiguities in both sectors cancel each other at the leading order in the double scaling limit. We thus clarify resurgence structure of the two-point functions in the supersymmetric double-well matrix model.