Cutting rules and perturbative unitarity of noncommutative electric-type field theories from string theory

TL;DR

This paper investigates how noncommutative electric-type quantum field theories violate perturbative unitarity by analyzing string theory loop amplitudes and their zero slope limits, revealing the emergence of unphysical tachyonic branch cuts.

Contribution

It provides a detailed string-theoretic analysis of unitarity breakdown in noncommutative electric field theories, connecting string amplitudes to noncommutative field theory pathologies.

Findings

Unphysical tachyonic branch cuts appear in noncommutative electric theories.

String theory analysis clarifies the origin of unitarity violation.

Insights into magnetic case complement the electric case discussion.

Abstract

We discuss the breakdown of perturbative unitarity of noncommutative quantum field theories in electric-type background in the light of string theory. We consider the analytic structure of string loop two-point functions using a suitable off-shell continuation and then study the zero slope limit of Seiberg and Witten. In this way we pick up how the unphysical tachyonic branch cut appears in the noncommutative field theory. We briefly discuss discontinuities and cutting rules for the full string theory amplitude and relate them to the noncommutative field theoretical results, and also discuss the insight one gains into the magnetic case too.