Multi-Instanton Calculus in c = 1 String Theory Bruno Balthazar, Victor A. Rodriguez, Xi Yin Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138 USA
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[email protected] Abstract We formulate a strategy for computing the complete set of non-perturbative correc- tions to closed string scattering in c = 1 string theory from the worldsheet perspective. This requires taking into account the effect of multiple ZZ-instantons, including higher instantons constructed from ZZ boundary conditions of type (m; 1), with a careful treatment of the measure and contour in the integration over the instanton moduli space. The only a priori ambiguity in our prescription is a normalization constant Nm that appears in the integration measure for the (m; 1)-type ZZ instanton, at each positive integer m. We investigate leading corrections to the closed string reflection am- plitude at the n-instanton level, i.e. of order e−n=gs , and find striking agreement with our recent proposal on the non-perturbative completion of the dual matrix quantum mechanics, which in turn fixes Nm for all m. arXiv:1912.07170v1 [hep-th] 16 Dec 2019 Contents 1 Introduction 1 2 Instanton expansion in the non-perturbative completion of the c = 1 matrix quantum mechanics 4 3 Multiple ZZ-instantons from the worldsheet perspective 8 3.1 ZZ boundary conditions and instantons . .9 3.2 The instanton measure . 11 3.3 2-instanton corrections to the closed string 1 ! k amplitude . 13 3.4 3-instanton corrections to the closed string 1 ! 1 amplitude .