Noncommutative perturbative quantum field theory: Wilson loop in two-dimensional Yang-Mills, and unitarity from string theory

TL;DR

This paper explores noncommutative quantum field theory derived from string theory, focusing on Wilson loop calculations in 2D NCYM, and investigates unitarity issues through string loop analysis and the Seiberg-Witten limit.

Contribution

It provides a detailed perturbative analysis of Wilson loops in 2D NCYM, compares different prescriptions, and discusses unitarity breakdown from a string theory perspective.

Findings

WML prescription yields well-defined Wilson loops in the commutative limit.

PV prescription results in singular Wilson loops, related to topological excitations.

Unitarity breakdown is linked to tachyonic branch cuts in string loop functions.

Abstract

The results of our research on noncommutative perturbative quantum field theory and its relation to string theory are exposed with details. 1) We give an introduction to noncommutative quantum field theory and its derivation from open string theory in an antisymmetric background. 2) We perform a perturbative Wilson loop calculation for 2D NCYM. We compare the LCG results for the WML and the PV prescription. With WML the loop is well-defined and regular in the commutative limit. With PV the result is singular. This is intriguing: in the commutative theory their difference is related to topological excitations, moreover PV provides a point-like potential. 3) Commutative 2D YM exhibits an interplay between geometrical and U(N) gauge properties: in the exact expression of a Wilson loop with n windings a scaling intertwines n and N. In the NC case the interplay becomes tighter due to the merging of space-time and ``internal'' symmetries. Surprisingly, in our up to O(g^6) (and beyond) crossed graphs calculations the scaling we mentioned occurs for large n, N and theta. 4) We discuss the breakdown of perturbative unitarity of noncommutative electric-type QFT in the light of strings. We consider the analytic structure of string loop two-point functions suitably continuing them off-shell, and then study the Seiberg-Witten limit. In this way we pick up how the unphysical tachyonic branch cut appears in the NC field theory.