New critical behavior in a supersymmetric double-well matrix model

TL;DR

This paper analyzes a supersymmetric double-well matrix model, revealing new critical behaviors and connecting it to two-dimensional quantum gravity, minimal string theory, and type IIA superstring theory, with implications for correlation functions and backgrounds.

Contribution

It introduces a novel supersymmetric matrix model with double-well potential, explores its critical behaviors, and establishes connections to string theories and quantum gravity.

Findings

Discovery of new logarithmic critical behavior in correlation functions.

Mapping of the model to the O(n) model on a random surface with n=-2.

Implication of a nontrivial Ramond-Ramond background in type IIA theory.

Abstract

We compute various correlation functions at the planar level in a simple supersymmetric matrix model, whose scalar potential is in shape of a double-well. The model has infinitely degenerate vacua parametrized by filling fractions \nu_\pm representing the numbers of matrix eigenvalues around the two minima of the double-well. The computation is done for general filling fractions corresponding to general two-cut solutions for the eigenvalue distribution. The model is mapped to the O(n) model on a random surface with n=-2, and some sector of the model is described by two-dimensional quantum gravity with c=-2 matter or (2,1) minimal string theory. For the other sector in which such description is not possible, we find new critical behavior of powers of logarithm for correlation functions. We regard the matrix model as a supersymmetric analog of the Penner model, and discuss correspondence of the matrix model to two-dimensional type IIA superstring theory from the viewpoint of symmetry and spectrum. In particular, single-trace operators in the matrix model are naturally interpreted as vertex operators in the type IIA theory. Also, the result of the correlation functions implies that the corresponding type IIA theory has a nontrivial Ramond-Ramond background.