Dynamical Aspects on Duality between SYM and NCOS from D2-F1 Bound State

TL;DR

This paper explores the duality between (2+1)-dimensional N=8 super Yang-Mills theory with electric flux and noncommutative open string theory, confirming their correspondence through effective actions and scattering amplitudes.

Contribution

It provides a detailed analysis of the duality by matching effective actions and scattering processes, including non-perturbative instanton effects, between SYM and NCOS theories.

Findings

Effective actions of probe M2-branes match between theories.

Scattering amplitudes in NCOS mirror instanton effects in SYM.

Velocity dependence behaviors are consistent across dual descriptions.

Abstract

It has been shown that (2+1)-dimensional N=8 super Yang-Mills (SYM) theory with electric flux is related to (2+1)- dimensional noncommutative open string (NCOS) theory by `2-11' flip. This implies that the instanton process in SYM theory, which corresponds to D0-brane exchange (M-momentum transfer) between D2-branes, is dual to the KK momentum exchange in NCOS theory, which is perturbative process in nature. In order to confirm this, we obtain the effective action of probe M2-brane on the background of tilted M2-branes, which would correspond to the one-loop effective action of SYM theory with non-perturbative instanton corrections. Then we consider the dual process in NCOS theory, which is the scattering amplitude of the wound graviton off the D2-F1 bound state involving KK-momentum transfer in x^2-direction. Both of them give the same interaction terms. Remarkably they also have the same behavior on the nontrivial velocity dependence. All these strongly support the duality between those two theories with completely different nature.