String field theory vertex from integrability

Abstract

We propose a framework for computing the (light cone) string field theory vertex in the case when the string worldsheet QFT is a generic integrable theory. The prime example and ultimate goal would be the $Ad{S}_5\times S^5$ superstring theory cubic string vertex and the chief application will be to use this framework as a formulation for $\mathcal{N}=4$ SYM theory OPE coefficients valid at any coupling up to wrapping corrections. In this paper we propose integrability axioms for the vertex, illustrate them on the example of the pp-wave string field theory and also uncover similar structures in weak coupling computations of OPE coefficients.

pdflatex, 52 pages, 20 figures,v2: references added, typos corrected

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• Hexagonalization of Correlation Functions
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Structure constants at wrapping order
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
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