Abstract
In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond–Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected by supersymmetry terminate at some finite order, whereas those of unprotected operators yield non-Borel summable series. The behavior of the latter is characteristic in string perturbation series, providing further evidence that the matrix model describes a string theory. Moreover, instanton corrections to the planar one-point functions are also computed, and universal logarithmic scaling behavior is found for non-supersymmetric operators.
Highlights
The fact that the Large Hadron Collider (LHC) was not able to observe any supersymmetric particles at the first run has made supersymmetry breaking predicted to occur at higher energy scale
By looking back on important roles played by supersymmetry in string theory, we are tempted to expect a possibility of spontaneous supersymmetry breaking in string theory
It is undoubtedly important to explore mechanisms of spontaneous supersymmetry breaking in lower-dimensional string theory, namely a toy model of the critical string theory
Summary
The fact that the Large Hadron Collider (LHC) was not able to observe any supersymmetric particles at the first run has made supersymmetry breaking predicted to occur at higher energy scale. In the previous work [1], we pointed out correspondence between a supersymmetric matrix model with the scalar potential of double-well type and two-dimensional type IIA superstring theory on a Ramond-Ramond background. In [2], it is explicitly checked by comparing planar correlation functions in the matrix model and those at the tree level in the type IIA superstring theory. It is expected that the matrix model nonperturbatively realizes the IIA superstring theory by taking its double scaling limit and enables nonperturbative investigation for the superstring theory. The operator (accompanied with operator mixing) corresponds to a vertex operator of Ramond-Ramond two-form field strength in the IIA theory This is not protected by supersymmetry, while the operator for even n is protected. They are obtained from correlation functions of the resolvent operators
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