Quasilocality of joining/splitting strings from coherent states

TL;DR

This paper uses coherent states to analyze the one-loop non-planar dilatation operator in ${ m N}=4$ SYM, revealing a scaling behavior that hints at a connection to string field theory interactions and proposing a toy model for string splitting and joining.

Contribution

It introduces a novel coherent state formalism to compute matrix elements and presents a solvable toy model for string interactions, highlighting their small contribution to energy shifts.

Findings

Matrix elements show a curious scaling behavior.

Qualitative similarity to string field theory vertices.

Splitting and joining contributions are small.

Abstract

Using the coherent state formalism we calculate matrix elements of the one-loop non-planar dilatation operator of ${\cal N}=4$ SYM between operators dual to folded Frolov-Tseytlin strings and observe a curious scaling behavior. We comment on the {\it qualitative} similarity of our matrix elements to the interaction vertex of a string field theory. In addition, we present a solvable toy model for string splitting and joining. The scaling behaviour of the matrix elements suggests that the contribution to the genus one energy shift coming from semi-classical string splitting and joining is small.