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 (9)

• Combinatorics of Boundaries in String Theory
• Strings from Tachyons
• Remarks on Liouville theory with boundary
• String Theory in Two Dimensions
• Exact S-Matrix for 2D String Theory
• Developments in 2D String Theory
• Classical Scattering in $1+1$ Dimensional String Theory
• ZZ Instantons and the Non-Perturbative Dual of c = 1 String Theory
• ZZ boundary states and fragmented AdS2 spaces

Cited by in corpus (11)

• Normalization of D-instanton Amplitudes
• D-instantons, String Field Theory and Two Dimensional String Theory
• Normalization of Type IIB D-instanton Amplitudes
• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• Muti-instanton Amplitudes in Type IIB String Theory
• Gauge-invariant operators of open bosonic string field theory in the low-energy limit
• The complex Liouville string: worldsheet boundaries and non-perturbative effects
• Nonperturbative definition of closed string theory via open string field theory
• String correlators on ${\text{AdS}}_3$: Four-point functions
• Asymptotically Free AdS3/CFT2
• Exact quantization and analytic continuation