Multi-instanton calculus in c = 1 string theory
Bruno Balthazar, Victor A. Rodriguez, Xi Yin
Abstract
A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> 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 $$ {e}^{-n/{g}_s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mspace/> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>n</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:msup> </mml:math> , and find striking agreement with our recent proposal on the non-perturbative completion of the dual matrix quantum mechanics, which in turn fixes $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> m for all m .