SYM ANOMALOUS DIMENSION FROM OPEN STRING ENGINEERED CURVATURE

Abstract

In the full type IIB open superstring setup, we show that there exists a vertex operator, denoted by VL, whose renormalization reproduces the same anomalous dimension matrix that was obtained by Minahan and Zarembo (MZ) [J. High Energy Phys. 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 nonlinear sigma model action in a D-brane background. Park [Phys. Lett. B 660, 583 (2008)] 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, VG, we show that the SYM result is reproduced. We comment on fermionic completion of VL and on how the special form of the non-Abelian vertex VG may arise.