SYM anomalous dimension from open string engineered curvature

TL;DR

This paper demonstrates how a specific vertex operator in open superstring theory reproduces the anomalous dimensions of SYM operators, linking string curvature effects to gauge theory results.

Contribution

It introduces a vertex operator in open superstring theory that reproduces SYM anomalous dimensions, highlighting the role of non-abelianized curvature terms.

Findings

Vertex operator $V_L$ reproduces MZ anomalous dimensions.

Non-abelianized curvature terms generate SYM results.

Special non-abelian vertex $V_G$ reproduces SYM anomalous dimensions.

Abstract

In the full type IIB open superstring setup, we show that there exists a vertex operator, denoted by $V_L$, whose renormalization reproduces the same anomalous dimension matrix that was obtained by Minahan and Zarembo (MZ) in {\em JHEP} {\bf 0303}, 013 (2003). The vertex operator is a gauge singlet, and has the same SO(6) index structure as the operator used by MZ. To obtain the SYM anomalous dimensions, one of the key ingredients is the non-abelianization of the non-linear sigma model action in a D-brane background. In {\em Phys.\ Lett.} {\bf B 660}, 583 (2008), it was conjectured that quantum effects of open strings on a stack of D-branes should generate the curvature. Even though the conjecture had passed a few consistency checks, the role of the higher order curvature terms has remain mostly unobserved until now. By choosing a special form of the non-abelianized counter vertex, $V_G$, we show that the SYM result is reproduced. We comment on fermionic completion of $V_L$ and on how the special form of the non-abelian vertex $V_G$ may arise.