Noncommutative N=2 p-p' System

TL;DR

This paper investigates the properties of noncommutative N=2 p-p' systems with magnetic backgrounds, revealing potential topological aspects and novel non-associative structures in the low-energy limit, and explores their relation to field theory.

Contribution

It analyzes open string amplitudes in noncommutative N=2 systems, uncovering local four-point functions and non-associative star products, suggesting a topological nature and connections to field theory.

Findings

Four-point function is local in the Seiberg-Witten limit.

Identifies non-associative generalized star products.

Suggests a topological interpretation of the theory.

Abstract

We analyse several open and mixed sector tree-level amplitudes in N=2 p-p' systems with a constant magnetic B turned on. The 3-point function vanishes on-shell. The 4-point function, in the Seiberg-Witten (SW) low energy limit\cite{SW}, is local, {\it indicating the possible topological nature of the theory (in the SW low energy limit)} and the {\it possible relation between noncommutative N=2 p-p' system in two complex dimensions and in the SW limit, and (non)commutative N=2 p'-p' system in two real dimensions.} We discuss three extreme noncommutativity limits (after having taken the Seiberg-Witten low energy limit) of the mixed 3-point function, and get two kinds of commutative non-associaitive generalized star products. We make some speculative remarks related to reproducing the above four-point tree level amplitude in the open sector, from a field theory.