Multi-Instanton Calculus in c = 1 String Theory

Abstract

We formulate a strategy for computing the complete set of non-perturbative corrections 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 ${\mathcal{N}}_m$ 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 amplitude at the $n$-instanton level, i.e. of order $e^{-n/g_s}$, and find striking agreement with our recent proposal on the non-perturbative completion of the dual matrix quantum mechanics, which in turn fixes ${\mathcal{N}}_m$ for all $m$.

29 pages, 6 figures

References in corpus (1)

• ZZ boundary states and fragmented AdS2 spaces

Cited by in corpus (2)

• Gauge-invariant operators of open bosonic string field theory in the low-energy limit
• Nonperturbative definition of closed string theory via open string field theory